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Variations of the Fraser River plume : observations and computer simulations Royer, Louise 1983

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VARIATIONS OF THE FRASER RIVER PLUME; SIMULATIONS OBSERVATIONS AND COMPUTER by LOUISE ROYER B.Sc., Universite de Montreal, 1979 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department Of Oceanography We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF July © Louise BRITISH COLUMBIA 1 983 Royer, 1983 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of 0c€(X Ifi 0 q KV) The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D E - 6 (3/81) i i Abstract Temporal and s p a t i a l variations of the Fraser River plume, in the central S t r a i t of Georgia ( B r i t i s h Columbia, Canada), are monitored by continuous s a l i n i t y sampling of the engine cooling water on two B.C. f e r r i e s . T r a v e l l i n g along two di f f e r e n t routes between Vancouver Island and the mainland the f e r r i e s provide eight crossings per day both north and south of the river outflow. From each crossing, c h a r a c t e r i s t i c measures of the plume are extracted, such as the average s a l i n i t y and the maximum s a l i n i t y gradient. These parameters are then formulated as time series and used to compute cross-correlations and cross-spectra with the probable driving forces of wind and river discharge. The ef f e c t of the tides i s examined using harmonic analysis. Periods of high r i v e r discharge lead to decreases in the average s a l i n i t y for each section, and peaks in the magnitude of the maximum s a l i n i t y gradient. The corr e l a t i o n of the plume c h a r a c t e r i s t i c s (average s a l i n i t y , maximum s a l i n i t y gradient) on the southern section with the along-strait component of the wind is consistent with advection by the wind. Weak cor r e l a t i o n i s found between the plume c h a r a c t e r i s t i c s on the northern section and the wind. Linear combination of the wind and the discharge variations reproduce the general trend of the average s a l i n i t i e s but cannot explain the l e v e l of v a r i a b i l i t y . A s h i f t to a non-linear combination of the wind and discharge improves t h i s comparison. The phases of parameter fluctuations at t i d a l frequencies, on the southern section, agree with the expected i effects of t i d a l currents and the modulation of the r i v e r discharge. The agreement i s not as apparent for the northern section. The l e v e l of the discharge i s seen to affect the t i d a l amplitudes of the s a l i n i t y fluctuations on the southern section. A numerical model, previously developed to examine the eff e c t of t i d a l forcing on the plume, is modified to input the hourly wind and da i l y discharge data record. Equivalent average s a l i n i t i e s along the ferry section are outputed and compared to the observed ferry data. Good agreement i s reached after manipulating the entrainment v e l o c i t y and the momentum transfer from the wind to the plume. The tides are seen to add a t i d a l modulation to the general s a l i n i t y pattern resulting from the combined e f f e c t of the wind and the discharge. Horizontal d i s t r i b u t i o n s from the model and from CTD cruise results agree f a i r l y well with each another. Table of Contents Abstract i i L i s t of Tables v i L i s t of Figures v i i Acknowledgements xi I. INTRODUCTION 1 I I . DATA COLLECTION AND PROCESSING 3 2.1 Data C o l l e c t i o n 3 2.2 Data Processing 7 2.2.1 Ferry Data 7 2.2.2 CTD Data 11 2.3 Error Estimation 11 2.3.1 Wind Forcing Parameter 11 2.3.2 Comparison Between The Ferry Data And The Lighthouse Data 13 2.3.3 Comparison Between The Ferry Data And The CTD Data 15 2.3.4 Comparison Of Data From Two Ferries On The Same Sect ion 18 I I I . VISUAL INTERPRETATION OF THE FERRY DATA 26 3.1 Comparison Of The Plume Cha r a c t e r i s t i c s With Discharge 26 3.2 Comparison Of The S a l i n i t y At Different Points Along The Sections 30 3.3 Comparison Of The Daily Variance Series 34 3.4 Combined E f f e c t s Of The Wind And Discharge On The Plume Characteristics 37 3.4.1 Spring 1980 37 3.4.2 December Peak 40 3.4.3 Spring 1981 41 IV. STATISTICAL ANALYSIS 44 4.1 Cross-correlations 44 4.1.1 Discharge 44 4.1.2 Wind 46 4.2 Linear And Non-linear Combination Of The Wind And Discharge .48 4.3 Spectra And Cross-spectra 57 4.3.1 Cross-spectra With The Discharge .59 4.3.2 Cross-spectra With The Wind 60 4.4 Harmonic Analysis 62 V. COMPUTER SIMULATIONS 69 5.1 Description Of An Existing Model Of The Fraser River Plume 69 5.2 General Modifications Of The Existing Model 72 5.3 Numerical Results With Variable Discharge And Wind Forcing 79 5.3.1 Comparison Of The Average S a l i n i t i e s 80 5.3.2 Quantitative Estimate Of The Agreement Between The Model And The Ferry Observations 96 5.4 Numerical Results Including T i d a l Forcing 100 5.5 Horizontal Distributions Of The Plume Properties .109 VI. CONCLUSIONS 127 V BIBLIOGRAPHY 131 v i L i s t of Tables I. Periods where the ferry data are available 5 II. Results of the s t a t i s t i c s of the average s a l i n i t y difference between two series recorded on two di f f e r e n t f e r r i e s on the same section 19 III. Amplitudes (A) and phase (#) from the harmonic analysis of the average s a l i n i t y series from d i f f e r e n t f e r r i e s on the same sections 21 IV. Results of the s t a t i s t i c s of the maximum s a l i n i t y gradient difference between two series recorded on two d i f f e r e n t f e r r i e s on the same section 23 V. Results of the cross-correlation computations between the plume c h a r a c t e r i s t i c s and the forcing parameters 45 VI. Averaged cross-correlation c o e f f i c i e n t s between the plume c h a r a c t e r i s t i c (Series 3), the discharge (Series 1), the wind (Series 2) and the linear combination (Series 4) 51 VII. Results of the cross-spectra between the plume c h a r a c t e r i s t i c s and the river discharge 59 VIII. Results of the cross-spectra between the plume c h a r a c t e r i s t i c s and the along s t r a i t wind component 61 IX. Amplitudes (A) in o/oo and phases (</>) from the harmonic•analysis done on the average s a l i n i t y series for the two years of the data 63 X. Cross-correlations and time lags between the average s a l i n i t i e s of the model and of the ferry data 97 XI. Root mean squared error (o/oo) between the model and the ferry data average s a l i n i t i e s 98 XII. Amplitudes and phases from the harmonic analysis of the average s a l i n i t y of the model and the ferry data 107 v i i L i s t of Figures 1. Map of the S t r a i t of Georgia with the following: 1: Fraser River, 2: Point Atkinson tide gauge, 3: Sand Heads wind station, 4: Entrance Island wind station and lighthouse station, 5: Active Pass lighthouse station. Dots on axes indicate positions of CTD stations 4 2. Plots of s a l i n i t y versus position for eight consecutive t r i p s on the northern section on June 9, 1980. Dots indicate the positions of the maximum horizontal s a l i n i t y gradients 9 3. Plots of s a l i n i t y vs time from a) the data measured at Entrance Island lighthouse b) the northern section d a i l y average ferry data at x=0 c) the data measured at Active Pass lighthouse d) the southern section d a i l y average ferry data at x=0 14 4. S a l i n i t y depth p r o f i l e obtained on May 11, 1981 at the second most eastern CTD station on the northern section 16 5. Histograms of the d i s t r i b u t i o n of ferry data s a l i n i t y depths from the analysis of a l l 231 CTD stations ( s o l i d line) and of 95 CTD stations (broken line) characterized by a v e r t i c a l s a l i n i t y difference equal or greater than 4 o/oo 17 6. Plots of the a) Fraser River discharge, b) the average s a l i n i t y on the northern section and c) the average s a l i n i t y on the southern section versus time 27 7. Plots of the a) Fraser River discharge, b) the maximum s a l i n i t y gradient along the northern section and c) the maximum s a l i n i t y gradient along the southern section versus time 29 8. Plots of s a l i n i t y versus time for f i v e d i f f e r e n t points along the southern section (x = 0, 1/3,1/2,2/3,1 ) ...31 9. Plots of s a l i n i t y versus time for five d i f f e r e n t points along the northern section (x=0,1/3,1/2,2/3,1) 32 10. Plots of the dail y variance of s a l i n i t y versus time for f i v e d i f f e r e n t points along the southern section (x = 0,1/3,1/2,2/3,1) 35 11. Plots of the dail y variance of s a l i n i t y versus time for f i v e d i f f e r e n t points along the northern section (x=0,1/3,1/2,2/3,1) ..36 12. Plot of the River discharge ( s o l i d l i n e , t o p ) , stick diagram of wind (top), and plots of average s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d line) and northern (broken line) sections vs time during the Spring 1980 38 13. Plot of the River discharge ( s o l i d l i n e , t o p ) , s t i c k diagram of wind (top), and plots of average v i i i s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d l ine) and northern (broken line) sections vs time during the December Peak 40 14. Plot of the River discharge ( s o l i d l i n e , t o p ) , s t i c k diagram of wind (top), and plots of average s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d l ine) and northern (broken line) sections vs time during the Spring 1981 42 15. Plots of northern section plume c h a r a c t e r i s t i c s versus time: a) average s a l i n i t y ferry data, b) average s a l i n i t y from linear combination, c) maximum s a l i n i t y gradient ferry data, d) maximum s a l i n i t y gradient from linear combination 53 16. Plots of southern section plume c h a r a c t e r i s t i c s versus time: a) average s a l i n i t y ferry data, b) average s a l i n i t y from linear combination, c) maximum s a l i n i t y gradient ferry data, d) maximum s a l i n i t y gradient from linear combination 54 17. Plots of the average s a l i n i t y versus time for the a) northern and b) southern sections as given by a non-linear combination of wind and discharge 56 18. Plots of normalized spectra of a)the Fraser River discharge, b) the along-strait wind component, c)the southern and d) northern section average s a l i n i t i e s and the e) southern and f) northern section maximum s a l i n i t y gradient 58 19. Northern (top) and southern (bottom) section s a l i n i t y fluctuation amplitudes for the ( s o l i d l i ne) and M2 (broken line) constituents from harmonic analyses done on nine d i f f e r e n t data portions characterized by a discharge l e v e l (L,M,H) .67 20. Grid used by the numerical model showing the two ferry tracks and the set of coordinates used 74 21. Dis t r i b u t i o n s of v e l o c i t y and s a l i n i t y used as i n i t i a l conditions. The s a l i n i t y contour labels have unit of o/oo and the t a i l of the ve l o c i t y vector i s located on the corresponding g r i d point ...76 22. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the December Peak using a model similar to the one of Stronach but with variable wind and discharge and no t i d a l forcing 81 23. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model similar to the one of Stronach but with variable wind and discharge and no t i d a l forcing 82 24. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model similar to the one leading to Fi g . 23 but with reduced entrainment v e l o c i t y 88 25. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time ix for the Spring 1980 using a model with the entrainment v e l o c i t y of Stronach and a reduced wind factor (b=1.) 90 26. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time for the Spring 1980 using a model with a reduced entrainment ve l o c i t y and a reduced wind factor (b=1) 91 27. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model with reduced entrainment ve l o c i t y and with a reduced wind factor (b=0.5) ; 92 28. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the December Peak using a model with reduced entrainment and with a reduced wind factor (b=0.l25) 94, 29. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1980 using a model with a reduced entrainment v e l o c i t y , a reduced wind factor (b=1) and with t i d a l forcing 104 30. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the December Peak using a model with a reduced entrainment, a reduced wind factor (b=0.125) and with t i d a l forcing 105 31. Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model with a reduced entrainment v e l o c i t y , a reduced wind factor (b=0.5) and with t i d a l forcing 106 32. Surface s a l i n i t y contour (o/oo) from the CTD cruise on May 7-8, 1980 (Julian days 127-128). The crosses indicate the positions of the CTD stations 110 33. Surface s a l i n i t y contour (o/oo) as given by the numerical simulation of the cruise of May 7-8, 1980 (Julian days 127-128). The crosses indicate the positions of the CTD stations 111 34. Surface s a l i n i t y contour (o/oo) from the CTD cruise on May 11-12, 1981 (Julian days 496-497). The crosses indicate the positions of the CTD stations 112 35. Surface s a l i n i t y contour (o/oo) as given by the numerical simulation of the cruise of May 11-12, 1981 (Julian'''days 496-497). The crosses indicate the positions of the CTD stations . 113 36. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 123 (May 3, 1980) 1 1 5 37. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 130 (May 10, 1980) 1 16 38. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given X by a numerical model with variable wind and discharge on Ju l i a n day 132 (May 12, 1980) 117 39. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 361 (December 27, 1980) ....119 40. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 365 (December 31, 1980) ....120 41. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on J u l i a n day 376 (January 11, 1981) 121 42. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 508 (May 23, 1981 ) 123 43. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 517 (June 1, 1981) 124 44. S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 523 (June 7, 1981) 125 xi Acknowledgement Among a l l the people that helped carrying through t h i s thesis project, I would l i k e , in p a r t i c u l a r , to acknowledge the suggestions and advice from a l l the committee members, and especially the guidance from my thesis supervisor, Dr W.J. Emery. I would also want to thank the many o f f i c e r s and employees of the B.C. Ferry Corporation who cooperated in the data c o l l e c t i o n , especially Messrs A. Ritchie and B. Bowring for their support and cooperation. The dedication of P. Nowlan contributed s i g n i f i c a n t l y to maintaining and processing the data. I am grateful to Dr J.A. Stronach for his permission to use his numerical model program and to Dr L.E. Giovando for sending me the lighthouse data. This research was supported f i n a n c i a l l y by the Canadian Natural Sciences and Engineering Research Council under i t s Strategic Grants Program for Ocean (Grant No. G0353) and through a Science 1967 scholarship. This support i s g r a t e f u l l y acknowledged. F i n a l l y , I would l i k e to thank my husband, P h i l i p Green, for his continued encouragement and moral support. 1 I. INTRODUCTION A remarkable feature, in the central S t r a i t of Georgia near Vancouver, B.C. i s a strong s a l i n i t y front marking the fresh water extent of the Fraser River plume. This front is often associated with a marked change in colour due to an abrupt increase in the suspended sediment concentration. Different aspects of the plume have been studied through a e r i a l pictures (Tabata,1972), s a t e l l i t e pictures (Feely and Lamb, 1979; Duffus and T i l l e y , 1978), drogue tracking surveys (Giovando and Tabata,1970; Cordes, 1977) and a numerical model (Stronach,1981). In the introduction to his work, Stronach (1977) l i s t s most of the relevant studies of the Fraser River plume and similar plumes and LeBlond in a l a t t e r review (waiting publication) updates the l i s t . Among the pertinent work, papers by Waldichuk (1957) and Tully and Dodimead (1957) gave a f i r s t q u a l i t a t i v e description of the S t r a i t of Georgia waters. Other plumes have also been investigated. The M i s s i s s i p i River plume received modelling attention (Wright and Coleman, 1971). The Connecticut River plume has been documented by Garvine (Garvine and Monk, 1974; Garvine, 1974 and 1977) who also gave a n a l y t i c a l (Garvine, 1979 a and b, 1981) and numerical (O'Donnel and Garvine, 1983) model of front a l plume dynamics. A l l of these studies dealt mainly with short-term variations (over a day or two) of the plume properties. The present study investigates the causes of the plume property variations over a wide range of time scales. The variations of the plume's s a l i n i t y front are measured along two a c r o s s - s t r a i t sections by instruments on 2 B r i t i s h Columbia f e r r i e s . This data c o l l e c t i o n system provides the f i r s t fast sampling long-term data record of the plume fluctuations. An attempt i s made to correlate these measured variatio n s of the s a l i n i t y front with possible d r i v i n g mechanisms: the discharge of the River, the wind and the tides. Cross-correlations, cross-spectra and harmonic analyses w i l l be used to quantify the possible relationships between variations in the plume c h a r a c t e r i s t i c s and the forcing parameters. An exi s t i n g numerical model w i l l be modified to account for the long-term fluctuations of the forcing mechanisms and for easy comparisons with the ferry data. 3 I I . DATA COLLECTION AND PROCESSING 2.1 Data Col l e c t i o n B r i t i s h Columbia f e r r i e s offer platforms that make frequent t r i p s (eight per day) crossing the S t r a i t of Georgia a l l year long. The two tracks in the central S t r a i t are shown in F i g . 1. Up to three f e r r i e s have been equipped with instruments to monitor the temperature and s a l i n i t y of the engine cooling water. The sea water intake i s located about two or three metres below the water l i n e depending on ferry load. The instrument i n s t a l l e d on each ferry was a Shipboard S a l i n i t y Recorder (SDL-12) made by Applied Microsystems Ltd. This instrument i s s p e c i f i c a l l y made for monitoring and recording temperature, conductivity and time every minute. The s a l i n i t y measurements of the SDL-12 have an accuracy of ±0.1 o/oo and a range of 0 to 40 o/oo while the temperature range i s -2 to 25°C with an accuracy of ±0.02°C. During each ferry crossing while the data are automatically recorded, the o f f i c e r s on the ferry f i l l e d out log sheets giving radar fixes at s p e c i f i c points along the ferry tracks. To estimate the time i t takes for the near surface water to be taken into the sea chest and t r a v e l to the sensor, manual surface samples were taken from the deck of the ferry, two or three times a month. Unfortunately the f e r r i e s do not run at night, leaving a 35% gap in the data every day. Various malfunctions of the instruments and extended dry docking of the f e r r i e s also increased the amount of missing data. Table I gives a l i s t of 4 1 2 4 ° W 1 2 3 ° W 1 2 4 ° W 1 2 3 ° W Figure 1 - Map of the S t r a i t of Georgia with the following: 1: Fraser River, 2: Point Atkinson tide gauge, 3: Sand Heads wind station, 4: Entrance Island wind station and lighthouse station, 5: Active Pass lighthouse station. Dots on axes indicate the positions of CTD stations periods for which the recording seems s a t i s f a c t o r y . J u l i a n days are set so that January 1,1980 corresponds to day 0 and that they continuously covered the two years of 1980 and 1981. Table I indicates that, for small periods of time, each section has been monitored by two f e r r i e s simultaneously. The ferry data give a horizontal d i s t r i b u t i o n of the plume 5 Table I - Periods where the ferry data are available Name of the ferry and section monitored S t a r t i n g - f i n i s h i n g dates Starting-Finishing Julian days Queen of Alberni (Southern section) 1980: March 21-July 16, Aug 1-Oct 21, Oct 24-Nov 23, Dec 18-Dec 24, Dec 26-Jan 9 1981. 1981: Jan 11-Feb 2,Feb 5-Feb 16,Feb 18-May 4, May 6, May 9-June 3, June 7-June 25, Sept 9-Nov 11. 80-197, 213-294,297-327,352-358, 360-374 376-398,401-412,414-489, 491,494-519, 523-541,617-680 Queen of Alberni (Northern section) 1981: June 26-Aug 28, Sept 1-Sept 8. 542-605, 609-616 Queen of Coquitlam (Northern section) 1980: Feb 22-March 12, March 15-March 20, March 25-July 4, July 8-Sept 7, Sept 10-Sept 30. 52-71, 74-79, 84-185,189-250,253-273 Queen of Cowichan (Northern section) 1980: Nov 21-Feb 20 1981 1981: March 24-April 4, A p r i l 16-Dec 16. 325-416 448-459, 471-715 Queen of Oak Bay (Southern section) 1981: July 24-Oct 6. 570-644 at one depth. In order to get some insight into the v e r t i c a l d i s t r i b u t i o n of the water properties of the plume, monthly CTD surveys have been carried out. Each survey consisted of 32 to 42 stations from which ten stations were along the northern ferry section and six stations covered the southern section (Fig. 1). The rest of the stations were dispersed in the area of the S t r a i t between the two ferry sections. Conductivity and temperature were measured by a Gui l d l i n e 8705 d i g i t a l CTD down to 100 metres, water depth permitting. A survey usually took 6 about 20 hours. In addition to the CTD surveys, surface temperature and s a l i n i t y were measured d a i l y at two lighthouses close to the path of the f e r r i e s . They are located at Entrance Island and Active Pass (Fig. 1). To evaluate the effects of the various forcing mechanisms, time series data of wind, tide and r i v e r discharge were acquired (Fig. 1). Hourly wind data are available from two stations maintained by the Atmospheric Environment Service: Entrance Island (4) and Sand Heads (3). The wind measurements are made to the nearest mile/hr with the d i r e c t i o n s p e c i f i e d by one of the eight directions of the compass card. The nearest tide gauge i s located at Point Atkinson (Fig. 1) (Canadian tide and current tables 1980, and 1981). The sea l e v e l elevation given at t h i s station can be used to characterize the tides for the entire study area (Crean,1976). The discharge of the Fraser r i v e r i s measured d a i l y by Water Survey of Canada at Mission City situated about 75 km upstream of the rive r mouth. There i s no station closer to the r i v e r mouth and i t was not possible to estimate the contributions of the small r i v e r s discharging into the Fraser River between Mission City and the r i v e r mouth. By looking at the r a t i o of the areas drained by these smaller r i v e r s to the area drained by the Fraser River, one can argue that the contributions of these t r i b u t a r i e s are small and that most of the variations in the rive r discharge are monitored at Mission City. i 7 2.2 Data Processing 2.2.1 Ferry Data It was necessary to convert the raw data into time series of some plume c h a r a c t e r i s t i c s that could be compared with coincident time series of wind, tide and discharge. The time recorded on the ferry was f i r s t corrected for a delay of about fi v e minutes due to the travel time between the water surface and the instrument. This delay was evaluated by comparing the manual surface s a l i n i t y samples to the s a l i n i t y recorded by the instrument. This corrected time was then converted to a position across the S t r a i t defined by a set of cartesian coordinates, unique to each section (Fig. 1). The x-axis follows the ferry track with x increasing towards the mainland. It should be noted that because of safety regulations, the track to Vancouver Island was set to be one nautical mile to the north of the one going to the mainland. The x-axes described here are set between these two tracks for each section; in other words, the y-coordinates of the ferry position averaged out to zero i f summed up over a long period of time. The length of the x-axes are 18 and 40 km for the southern and northern section, respectively. A pa r t i c u l a r position was usually normalized as the r a t i o of i t s x-coordinate in kilometres to the length of the axis. The y-coordinate was neglected. Assuming a constant speed between radar fi x e s , the s a l i n i t y as a function of position was plotted for the eight t r i p s per day. The usual picture (Fig. 2) i s a decrease of s a l i n i t y with 8 increasing x (as expected, since the Fraser River i s on the mainland). There i s also a sharp s a l i n i t y gradient on the order of 2 (o/oo)/km that marks the plume front. From each t r i p , the s a l i n i t y values at the mid-point, at one-third and two-thirds were extracted along with the average s a l i n i t y over the section and the magnitude, s a l i n i t y and position of the maximum gradient. These were then plotted against time, selected to be an average of the times when the ferry was at the ends of the section. Daily series of the c h a r a c t e r i s t i c s are needed for comparison with the discharge. The two data records on periods where two f e r r i e s were monitoring the same section simultaneously were f i r s t combined to give one time series. To account for gaps at night, hourly series were f i r s t interpolated using a tensioned cubic spline function (Spath,l969) and then convolved with a 48-h wide B a r t l e t t lag window. The value used for the d a i l y series was the smoothed value at noon of each day. In obtaining t h i s value, the averaging had put more weight on the measured values during the day than to the spline interpolated values during the night gaps. Interpolation of the d a i l y series with a cubic spline over gaps of 10 days or less was performed to provide series that cover a longer time i n t e r v a l than the individual hourly series. Formulated also as a d a i l y series was the variance of the s a l i n i t y estimates for each day at one point. It consists of the average of the squared differences between the s a l i n i t y at a fixed point and the d a i l y average of the s a l i n i t y at that point. 9 3 5 r 0 o o o >-< 3 5 r 0 N O R T H E R N S E C T I O N Fe r r y C r o s s i n g T ime 7=20 0 10 2 0 3 0 4 0 x = A c r o s s s t r a i t d is tance, km 9=10 11 = 2 0 13=10 15=20 17:10 19:20 21=10 F i g u r e 2 - P l o t s of s a l i n i t y versus p o s i t i o n f o r e i g h t c o n s e c u t i v e t r i p s o n t h e northern s e c t i o n on June 9, 1980. Dots i n d i c a t e the p o s i t i o n s of the maximum h o r i z o n t a l s a l i n i t y g r a d i e n t s 10 F i n a l l y the plume c h a r a c t e r i s t i c series were plotted and compared with each other and with the concurrent forcing parameter series (discharge and wind). Cross-correlations and cross-spectra were computed for various combinations of the plume c h a r a c t e r i s t i c s and the forcing parameters. Before computing each cross-correlation, a linear detrending of both time series was performed. The c h a r a c t e r i s t i c s chosen for these computations were the average s a l i n i t i e s and the magnitudes of the maximum s a l i n i t y gradient for both sections. The longest possible d a i l y series were used. They consist, for the southern section, of data for the periods from Julian days 80 to 327, 352 to 541 and 570 to 680. Similar time series for the northern section cover periods from Julian days 52 to 273, 325 to 416 and 448 to 715. Spectra were normalized (the power spectral estimates were divided by the variance of the series) to allow comparisons between spectra. In computing the spectra, a Ba r t l e t t taper function (Jenkins and Watts, 1968) with a width of 1/8 of the data series length was used as a f i l t e r . This procedure yielded 24 degrees of freedom for each spectral estimate. The noise l e v e l for the cross-spectra was estimated by using the n u l l hypothesis (Groves and Hannan, 1968). Harmonic analysis was used for comparisons at t i d a l frequencies, in place of the cross-spectra, to overcome the problem of interpolation. This analysis was intended to be ca r r i e d out for a l l t i d a l constituents for which the length of the record would allowed resolution. The computer program used was developed by Foreman and Henry ( 1979)°. This program, when 11 used with series of a year or two was too costly . It was then decided to exclude a l l the constituents for which the amplitude of the sea l e v e l elevation at Point Atkinson was smaller than .8 cm. P! was inferred from R , f r o m N 2 and K 2 from S 2 whenever the length of the record did not allow their resolution. The harmonic analysis has been performed on the four chosen c h a r a c t e r i s t i c s and for the sea le v e l elevation at Point Atkinson. The l a t t e r w i l l be used as a reference for the phases. These phases w i l l be expressed as the difference between the Greenwich phase lag of one of the four c h a r a c t e r i s t i c s and the Greenwich phase for the same constituent from the sea le v e l elevation. 2.2.2 CTD'Data The data from each 100m CTD drop were f i r s t sorted by increasing depth (using both up and down traces) then interpolated every 0.01 m and f i n a l l y smoothed by convolving the series of s a l i n i t y as a function of depth with a B a r t l e t t lag window of 1m width centered at each 0.5 m from 0.5 to 20 m. 2.3 Error Estimation 2.3.1 Wind Forcing Parameter The aim of thi s subsection i s to define a wind forcing parameter series that w i l l be used in the cross-correlations with the plume c h a r a c t e r i s t i c s . The prevailing winds are in general along the axis of the S t r a i t , northwest and southeast as discussed in Waldichuk (1957). For thi s reason the wind data 1 2 were separated into along-strait (positive towards the northwest) and a c r o s s - s t r a i t (positive towards the northeast) components. Spectra, cross-spectra and cross-correlations have been evaluated for the available two years of hourly wind data at the two coastal stations. No s t a t i s t i c a l differences were found between the two years of data. Spectra indicated sharp peaks at the diurnal frequency with t h i s frequency being r e l a t i v e l y more important for the a c r o s s - s t r a i t component. Broad peaks were also found at low frequencies. High values of the cross-c o r r e l a t i o n (0.8) near 0 lag, between the along-strait components at the two d i f f e r e n t stations, indicated the s p a t i a l uniformity of t h i s component over the central S t r a i t . The corresponding cross-spectra showed a r e s t r i c t i o n of th i s agreement to fluctuations with periods greater than 20 h. The ac r o s s - s t r a i t components were not as well correlated (0.3) and high coherencies were r e s t r i c t e d to periods between 31 h and 8 days with the exception of the diurnal frequency for which an out-of-phase relationship between the a c r o s s - s t r a i t components on each side of the S t r a i t seems to p r e v a i l . It was also found that the variance of the a c r o s s - s t r a i t component i s in general four times smaller than the along-strait component variance and that the two components were not independent. A small but s i g n i f i c a n t out-of-phase co r r e l a t i o n (0.2) was discovered for periods of the order of 3 to 10 days. From a l l these considerations, a single representative time series of the along-strait wind component seemed to be the 13 a p p r o p r i a t e q u a n t i t y to simulate the g l o b a l a c t i o n of the wind over the S t r a i t . The data from the wind s t a t i o n at Entrance I s l a n d w i l l be g e n e r a l l y used s i n c e i t i s the most complete r e c o r d . D a i l y wind s e r i e s were obtained from the h o u r l y data the same way as the d a i l y plume c h a r a c t e r i s t i c s e r i e s . 2.3.2 Comparison Between The F e r r y Data And The Lighthouse Data The next que s t i o n i s how w e l l do the f e r r y data d e s c r i b e the n e a r - s u r f a c e water p r o p e r t i e s . Sporadic and short s e r i e s of manual s u r f a c e sampling from the f e r r y deck gave an i n d i c a t i o n that the water monitored by the instrument had a higher s a l i n i t y than the s u r f a c e water by 1 to 2 o/oo. A comparison over a longer p e r i o d can be c a r r i e d out using the l i g h t h o u s e data. F i g . 3 shows the l i g h t h o u s e data along with the d a i l y s a l i n i t y at the' c l o s e s t p o i n t to the l i g h t h o u s e on the f e r r y t r a c k s , namely at x=0 on both s e c t i o n s . The e r r a t i c appearance of the s a l i n i t i e s measured at the l i g h t h o u s e s comes from the f a c t that t h i s d a i l y measure i s not smoothed and i s taken at d i f f e r e n t times each day. The s a l i n i t i e s measured by the f e r r y are u s u a l l y higher (on the average, by 0.6 o/oo on the southern s e c t i o n and by 0.06 o/oo on the northern s e c t i o n ) c o n s i s t e n t with the r e a l i z a t i o n that the f e r r y monitored water s l i g h t l y below the s u r f a c e . As c o u l d be seen by a v i s u a l i n s p e c t i o n of the time s e r i e s of F i g . 3, h i g h values f o r the c r o s s -c o r r e l a t i o n s of the two d i f f e r e n t estimates of the s u r f a c e s a l i n i t y were obtained (0.7 f o r both s e c t i o n s ) . These r e s u l t s show that the F e r r y s a l i n i t y data are r e p r e s e n t a t i v e of the near 1 4 1980 1981 fl) B) O O \ CJ cr CO m a a 0.0 a _ m r 1 5 . 0 TIME 30.0 45. (JULIAN DRY) (X10 ] 60, ) 1 75. O.D a 1 I T 15.0 30.D 45.0 TIME (JULIAN DAY) (X10 ] 60.0 ) 75.0 in 0.0 D) a . ~ l 15.0 TIME ~ ~ i — 30.0 (JULIAN o a I 1 45.0 60 0 DAY) (X-10 ] ) 75.0 o . o 15.0 TIME 1 30.0 (JULIAN i 1 — 45.0 60 0 DAY) (X10 3 ) 75.0 Figure 3 - Plots of s a l i n i t y vs time from a) the data measured at Entrance Island lighthouse b) the northern section d a i l y a v e r a g e ferry data at x=0 c) the data measured at Active Pass lighthouse d) the southern section d a i l y average ferry data at x=0 1 5 surface s a l i n i t y v a r i a t i o n s . 2.3.3 Comparison Between The Ferry Data And The CTD Data The aim of this subsection i s to establish the depth of the water monitored by the ferry. For th i s purpose an interpolated s a l i n i t y value was computed from the ferry crossing at the time a CTD station was taken from the values of s a l i n i t y along the ferry track from the two closest data points. A t y p i c a l s a l i n i t y depth p r o f i l e ( Fig. 4) monotonically increases with depth. From this p r o f i l e , the 0.5m depth-interval, within which the interpolated ferry s a l i n i t y i s found,constitutes an estimate of the depth from which the water monitored by the ferry was taken. Two hundred and t h i r t y one CTD stations were suitable for t h i s c a l c u l a t i o n (they were deployed within the ferry period of operation). The histograms of F i g . 5 summarize the r e s u l t s . The s o l i d l i n e histogram gives the percentage of the 231 stations defining the depth of the ferry s a l i n i t y for each 0.5m depth-interval within the f i r s t 20m of the water column. It shows that one t h i r d of the stations yielded a depth of the observed s a l i n i t y within the f i r s t 0.5m, that 80 % of the time the depth of th i s s a l i n i t y is within the f i r s t 7m and that the average depth i s 3.5m. This c l e a r l y indicates that the water monitored by the ferry corresponds to a near surface water type. Since the ferry intake was about 2 to 3m below the water l i n e , one could conclude that a great deal of v e r t i c a l mixing by the ferry brings the fresh surface water to the depth of the intake. A small fraction of the CTD stations yielded depths well 16 1 5 . 0 1 8 . 0 SALINITY (O/OO) 21 .0 30 .0 Figure 4 - S a l i n i t y depth p r o f i l e obtained on May 11, 1981 at the second most eastern CTD station on the northern section below the water intake (3% of the depths are below the 20 m l i n e ) . These anomalous depths are associated with stations having low v e r t i c a l s a l i n i t y gradients. For these stations, a small error in the estimation of the interpolated ferry s a l i n i t y produces a large variation in the estimated depth of the water 17 CD L U CD C E c o c\i L U C J Q _ CD O "I i - h l " h n n o.o 8.0 D E P T H (M) 16.0 Figure 5 - Histograms of the d i s t r i b u t i o n of ferry data s a l i n i t y depths from the analysis of a l l 231 CTD stations ( s o l i d line) and of 95 CTD stations (broken line) characterized by a v e r t i c a l s a l i n i t y difference equal or greater than 4 o/oo 18 having t h i s s a l i n i t y . The v a r i a t i o n of t h i s depth can be w e l l demonstrated f o r s t a t i o n s f o r which two s a l i n i t y estimates are a v a i l a b l e because two f e r r i e s were monitoring the same s e c t i o n at the time of the deployement of the CTD s t a t i o n . The d i f f e r e n c e i n the depths ranged from 0 to above 20 m with 80% of the d i f f e r e n c e s between 0 and 6.5 m. A new histogram (broken l i n e histogram of F i g . 5) was produced u s i n g only 95 s t a t i o n s f o r which a s a l i n i t y d i f f e r e n c e of 4 o/oo and over was observed in the f i r s t 20 m. The p r o p o r t i o n of the depths between 0 and 0.5 m d i d not change but the depths over 20 m disappeared because they corresponded to s t a t i o n s that monitored w e l l mixed water. A l a r g e r f r a c t i o n of the depth values than before were found at small depths (80% of them were above the 4.5 m depth l i n e and the average depth was 2.5 m). These v a l u e s of depth are known from CTD depth p r o f i l e s to be w i t h i n the depths i n f l u e n c e d by the plume ( F i g . 4). 2.3.4 Comparison Of Data From Two F e r r i e s On The Same S e c t i o n I t i s c r u c i a l to know the e r r o r s a s s o c i a t e d with the v a r i a t i o n s of the f e r r y l oad, the change of the f e r r y t r a c k s ( a l o n g - s t r a i t f l u c t u a t i o n s ) , the change of the f e r r y , changes i n the sampling depth, e t c . The r e p r o d u c i b i l i t y of the f e r r y r e s u l t s can be estimated by comparing the f e r r y data from two f e r r i e s m onitoring the same s e c t i o n at the same time. As i n f e r r e d from Table I, the northern s e c t i o n was simultaneously monitored by two f e r r i e s from J u l i a n days 542 to 605 and 609 to 616 and the southern s e c t i o n from J u l i a n days 617 to 644. 19 From the two average s a l i n i t y series for each section, hourly and d a i l y series were computed and the differences between the two s a l i n i t y estimates evaluated (Table I I ) . The Table II - Results of the s t a t i s t i c s of the average s a l i n i t y difference between two series recorded on two di f f e r e n t f e r r i e s on the same section Averaged difference of s a l i n i t y (o/oo) Root mean squared error (o/oo) Southern section Alberni - Oak Bay Series series hourly series Julian days: 617-644 0.5 1 .3 da i l y series Julian days: 617-644 0.5 1 .0 Northern section Cowichan - Alberni Series Series hourly series Julian days: 542-605 -0.2 1 .0 hourly series Julian days: 609-616 -0.5 1 .2 da i l y series Julian days: 542-616 -0.2 0.5 average difference of 0.5 o/oo for the southern section indicates that the s a l i n i t y values given by the instrument on the Queen of Alberni were s l i g h t l y higher than the ones from the Queen of Oak Bay. The two values of -0.2 and -0.5 o/oo of the average differences for the northern section account also for 20 the higher s a l i n i t y measured by the Queen of A l b e r n i than by the Queen of Cowichan. T h i s systematic e r r o r does not account f o r the root mean squared e r r o r between the two s e r i e s . The d a i l y averaging p r o c e s s , by smoothing the s e r i e s , decreases the RMS e r r o r . The e r r o r f o r the southern s e c t i o n i s i n g e n e r a l higher than f o r the other s e c t i o n . T h i s can be e x p l a i n e d by the p r o x i m i t y of the southern s e c t i o n to the F r a s e r r i v e r mouth that p r o v i d e s the p o s s i b i l i t y of s t r o n g s a l i n i t y d i f f e r e n c e s between the measurements from the two d i f f e r e n t f e r r i e s . In summary, the o v e r a l l s a l i n i t y e r r o r estimate i s on the order of 1 o/oo, which i s one order of magnitude l a r g e r than the accuracy of the instrument. T h i s e r r o r depends on the smoothing and on the f e r r y s e c t i o n used and i s s t i l l small compared to the s a l i n i t y f l u c t u a t i o n s which can be on the order of 10 o/oo. C r o s s - s p e c t r a between the two s a l i n i t y estimate s e r i e s were then computed to i n v e s t i g a t e the range of f r e q u e n c i e s f o r which the two s e r i e s agree with each other. C r o s s - s p e c t r a with h o u r l y s e r i e s i n d i c a t e d c o h erencies w e l l above the noise l e v e l f o r p e r i o d s higher than 30 hours. The c r o s s - c o r r e l a t i o n c o e f f i c i e n t s between the d a i l y s e r i e s were above 0.96 at day l a g 0. Confidence from these r e s u l t s i s a c q u i r e d s i n c e , f o r p e r i o d s above 30 h, the f e r r y s a l i n i t i e s g i v e r e p r o d u c i b l e measurements and the f l u c t u a t i o n s recorded at these f r e q u e n c i e s are independent of the f e r r y used. For the time p e r i o d when two f e r r i e s were monitoring the same s e c t i o n , one d a i l y s e r i e s can be computed from a combination of the s e r i e s from the two f e r r i e s s i n c e both s e r i e s d i s p l a y the same f l u c t u a t i o n s at the 21 same time. Prior to the combination, one of the series i s alter e d by the small amount i d e n t i f i e d as the systematic error between the two ferry measurements. For periods lower than 30 hours, such as t i d a l frequencies, harmonic analysis was used on the s a l i n i t y estimate series for each section. The results of these computations are compiled in table III for the constituents which at some point had an Table III - Amplitudes (A) and phase (<j>) from the harmonic analysis of the average s a l i n i t y series from d i f f e r e n t f e r r i e s on the same sections Alberni Oak Bay Cowichan Alberni series series series series (S. Section) (N. Section) Julian days: Julian days: Julian days: Julian days: 617--644 617--644 542--616 542--616 A <t> A <t> A <t> A <t> (o/oo) (°) (o/oo) (°) (o/oo) (°) (o/oo) (°) MSf 1 .3 136 0.7 101 0.9 235 0.8 219 2Qi 0.6 158 0.2 1 27 0.2 219 0.3 239 NO, 1 . 1 175 0.9 179 0.3 71 0.3 63 Pi 0.2 -21 0.5 -37 0.2 32 0.2 -20 K, 0.6 -21 1 .5 -37 0.5 32 0.6 -20 0.9 -38 0.6 -9 0.1 -68 0.1 -67 OO, 0.6 273 0.4 236 0.0 1 10 0.2 93 N 2 0.5 -34 0.1 -45 0.1 1 30 0.2 157 M2 0.7 -34 0.2 22 0.1 1 67 0.1 1 40" S 2 0.1 19 0.4 74 0.3 240 0.5 176 amplitude equal to or greater than 0.5 o/oo. For an error of 1 o/oo, in the s a l i n i t y measurements, only amplitudes equal to or above 0.5 o/oo could be thought of as being something other than noise. The s i m i l a r i t y between the results of the P, and the K, constituents are due to the inference of P, from K«. The absolute value difference between the two phase estimates for 22 each constituent never exceeds 64°. This value gives us an estimate on how well the phases from the harmonic analysis of the average s a l i n i t y can vary due to the sampling method. The exact same procedure can be applied to the two series of the magnitude of the maximum s a l i n i t y gradient from d i f f e r e n t f e r r i e s on each section. The accuracy of the instrument to measure horizontal s a l i n i t y gradients can be computed from the distance t r a v e l l e d by the ship during a sampling i n t e r v a l of 1 minute (0.7 km) and from the accuracy of the s a l i n i t y measurement (0.1 o/oo) to give an accuracy for the s a l i n i t y gradient of 0.1 (o/oo)/km. Table IV shows the analogous results to table III for the magnitude of the maximum gradient. As for the s a l i n i t y , the root mean squared error for the gradient i s above the accuracy of the instrument but the average error difference i s not s i g n i f i c a n t l y d i f f e r e n t from 0. This means that each ferry does not introduce an offset r e l a t i v e to the measurements of s a l i n i t y gradient from another f e r r y . As before the d a i l y averaging reduces the RMS error by smoothing. Both sections seem to produce the same error, that i s about 0.5 (o/oo)/km for hourly value ser i e s . Relative to the size of the maximum s a l i n i t y gradient that usually never exceeds 2 (o/oo)/km, t h i s error of 0.5 (o/oo)/km i s quite substantial. The cross-spectra between the two s a l i n i t y gradient estimates reached coherencies lower than those between the corresponding s a l i n i t y s e r i e s . The coherencies stay above the noise l e v e l for periods larger than 24 h for the northern section and 45 h for the southern section and the correlation 23 Table IV - Results of the s t a t i s t i c s of the maximum s a l i n i t y gradient difference between two series recorded on two di f f e r e n t f e r r i e s on the same section Averaged di fference of s a l i n i t y gradient (o/oo)/km Root mean squared error (o/oo)/km Southern section Alberni - Oak Bay Series series hourly series J u l i a n days: 617-644 0.1 0.5 da i l y series J u l i a n days: 617-644 0.1 0.2 Northern section Cowichan - Alberni Series Series hourly series J u l i a n days: 542-605 -0.1 0.5 hourly series J u l i a n days: 609-616 0.3 0.4 da i l y series J u l i a n days: 542-616 -0.1 0.3 c o e f f i c i e n t s for the da i l y series are 0.8 and 0.86 for the northern and southern section respectively. This supports the assumption that the variations of the magnitude of the maximum gradient, with periods over two days, are s i g n i f i c a n t l y well described by the ferry data. The harmonic analysis of the maximum s a l i n i t y gradient gave poor r e s u l t s . According to the RMS error, only t i d a l amplitudes 24 over 0.25 (o/oo)/km can be d i f f e r e n t i a t e d from noise. It only occured twice; that i s , for the constituent for the Oak Bay s a l i n i t y gradient series and the MSf constituent for the southern section Alberni ser i e s . A phase difference of 134° between the constituent of the Oak Bay series and the analogous Alberni series rules out the usefullness of this c h a r a c t e r i s t i c at t h i s t i d a l frequency. The MSf constituent leads to phase differences of 59° and 21° between the analogous s a l i n i t y gradient series for the southern and northern section, respectively. This constituent s t i l l holds the p o s s i b i l i t y of giving s i g n i f i c a n t information. It was then supposed that a better s a l i n i t y gradient c h a r a c t e r i s t i c , for short term variations, would be the magnitude of the s a l i n i t y gradient following a p a r t i c u l a r front instead of taking the maximum s a l i n i t y gradient for the whole section. This would d i f f e r e n t i a t e between the 1 to 3 fronts possibly present over a section at any one time. Such p a r t i c u l a r fronts were followed for the period of time when two f e r r i e s were monitoring the same section. The s a l i n i t y gradient and the position of the front were recorded as a time series. This procedure cuts the period of observation into small series of the length of the l i f e - t i m e of each front i . e . of the order of 10 days. The small length of these series makes them useless in the determination of long term variations but harmonic analysis can s t i l l be used. The analysis done with the fr o n t a l magnitude of the s a l i n i t y gradient did not show any improvement over the previous s a l i n i t y gradient c h a r a c t e r i s t i c . The MSf 25 constituent could not be resolved in the case of the frontal southern section s a l i n i t y gradient and position series and a large phase difference (106°) between the analogous fron t a l northern section s a l i n i t y gradient series was found. The la s t statement does not hold for the northern section frontal position series for which a phase difference of 17° was computed. The RMS errors for the position series were evaluated as being 4.7 and 3.3 km for the northern and southern section, respectively. 26 II I . VISUAL INTERPRETATION OF THE FERRY DATA 3.1 Comparison Of The Plume Characteristics With Discharge Marked ef f e c t s of the fluctuations in the Fraser River discharge on the average s a l i n i t y for both ferry sections can be seen by comparing the three d a i l y time series of F i g . 6. In general, both average s a l i n i t i e s show the same response, with lower s a l i n i t i e s corresponding to higher discharges in the springs and summers. Increases in river discharge occur rather rapidly in A p r i l and May (Julian days 110 to 130 and 475 to 515) while the adjustment to lower s a l i n i t i e s along the ferry sections i s somewhat slower. A l l three curves exhibit peaks (drops in s a l i n i t y ) in the early summer (Julian days 130 to 180 and 515 to 525) with a more gradual decrease in r i v e r discharge in the f a l l accompanied by gradual increases in s a l i n i t y . Along with the general decrease in average s a l i n i t i e s , both ferry sections display higher v a r i a b i l i t y during periods of high discharge. The amplitude of th i s v a r i a b i l i t y i s larger for the southern section r e f l e c t i n g i t s nearness to the Fraser River. This sharp response on the southern section to the discharge makes i t easier to see the effects of small peaks in the river discharge. Secondary peaks in discharge on Julian days 234, 254, 269, 278, 393 and 675 correspond to simultaneous drops in the southern section average s a l i n i t y . Similar drops are not evident in the northern section s a l i n i t y series except perhaps for the drop on day 675 that i s a r e l a t i v e l y large secondary peak. Some of the v a r i a b i l i t y of these s a l i n i t y estimates i s 27 1980 1981 fl) B) U J CD OC CE H C J CO O O o >-CE CO UJ CD t o • -O a • ' a o a 0.0 i — CJ UJ t n o 0.0 i — CJ UJ i n o CD ~] 15.0 TIME 30.0 45.0 ( J U L I A N DAT) ( X 1 0 ] 60.0 15.0 TIME 30.0 45.0 60.0 ( J U L I A N DAY) ( X 1 0 ] ) 75.0 75.0 0.0 "1 15.0 TIME 1 i 1 — 30.0 45.0 60.0 ( J U L I A N DAT) ( X 1 0 ] ) 75.0 Figure 6 - P l o t s of the a) Fraser River discharge, b) the average s a l i n i t y on the northern section and c) the average s a l i n i t y on the southern section versus time 28 due to wind forcing. The wind, as w i l l be seen l a t e r , contributes fluctuations ranging from 11.5 to 28 o/oo for the average s a l i n i t y on the southern section during the period of highest discharge for these two years (Julian days 515 to 525). An unusual feature of the curves in F i g . 6 is the abnormally high discharge in December 1980 and the corresponding drops in average s a l i n i t y along each ferry section. This event was due to anomalous rains and flooding in the winter of 1980/81. It i s interesting to note that although the maximum Fraser River discharge occured at day 361, the s a l i n i t y minima occured at days 365 and 363 at the southern and northern sections, respectively. With the close proximity of the southern section to the Fraser River mouth, i t i s a surprise that the more distant northern section responded f i r s t . In a subsequent subsection, t h i s p a r t i c u l a r event w i l l be discussed in d e t a i l r e l a t i n g the combined ef f e c t s of discharge and wind. The r i v e r discharge not only influences the average s a l i n i t i e s in the S t r a i t but also the horizontal gradients of s a l i n i t y , as can be seen in F i g . 7. In general, the magnitude of the maximum gradient on the southern section i s larger than that on the northern section. This again r e f l e c t s the proximity of the southern section to the Fraser River mouth. The previously mentioned secondary peaks in the discharge (on days 234, 254, 269, 278, 393 and 675) cause r e l a t i v e l y stronger magnitudes of the maximum gradient on the southern section. Other q u a l i t a t i v e patterns of the discharge are reproduced in the variations of the magnitude of the maximum gradient, l i k e 29 1980 1981 r 1 R) o i i i r 1 1 D.D 15.D 30.0 45.0 60.D 75.D TIME (JULJRN DAT) (X10 3 ) O.D 15.D 30.D 45.D 60.D 75.D TIME (JULIAN DAY] (X10 ] ) Figure 7 - Plots of the a) Fraser River discharge, b) the maximum s a l i n i t y gradient along the northern section and c) the maximum s a l i n i t y gradient along the southern section versus time 30 the sharp peak around day 360 and the low g r a d i e n t s around days 100, 300, 450 and 710 c o i n c i d e n t with the lowest values of the dis c h a r g e f o r the two y e a r s . 3.2 Comparison Of The S a l i n i t y At D i f f e r e n t P o i n t s Along The  S e c t i o n s The same p a t t e r n as that f o r the average s a l i n i t y i s reproduced i n the s a l i n i t i e s at some f i x e d p o i n t s a c r o s s each s e c t i o n . They are presented i n F i g s . 8 and 9 f o r f i v e p o i n t s along each of the southern and northern s e c t i o n s , r e s p e c t i v e l y . Q u a l i t a t i v e agreement between the v a r i a t i o n s of the s a l i n i t y at d i f f e r e n t p o i n t s along the s e c t i o n s suggests that the average s a l i n i t y was a good c h o i c e as a c h a r a c t e r i s t i c t h a t summarizes the s a l i n i t y f o r the whole s e c t i o n . In g e n e r a l , the s a l i n i t i e s i n c r e a s e from the mainland to Vancouver I s l a n d with the exception of the s a l i n i t y at the ea s t e r n end of the southern s e c t i o n that i s n o t i c e a b l y higher than the average s a l i n i t y f o r that s e c t i o n i n s p i t e of i t s pr o x i m i t y to the Fr a s e r R i v e r mouth. I t i s l i k e l y that the plume turns north, d e f l e c t e d by the C o r i o l i s a c c e l e r a t i o n , a d v e c t i n g the f r e s h water away from the southeast c o a s t . The s a l t y s u r f a c e water c l o s e to the east-end of the southern s e c t i o n has a l s o been observed dur i n g the CTD surveys done i n t h i s area and i s p r e d i c t e d by a numerical model as w i l l be seen i n chapter 5. Another p o s s i b l e e x p l a n a t i o n f o r the high s a l i n i t i e s measured by the f e r r i e s at the southeast terminus, depends on the o p e r a t i o n of the f e r r y . As can be seen from the 31 II X II X O cc O \ O fN II X CE CO II X a II x D . 0 1980 1981 f i i i i i D.D 15.D 30.D 45.0 TIME (JULIAN DAY) (X. 1 I 60.0 75 ! 0 ] ) i I 0.0 15.0 30.0 TIME (JULIA i 45.0 N DAY) (X. 1 1 60.0 75 10 ] ) i i i 0.0 15.0 30.0 45.0 TIME (JULIAN DAY) (X. 1 ! 60.0 75 10 ] ) i i i i i 0.0 15.0 30.0 45.0 60.0 75 TIME (JULIAN DAY) (X10 ] ) i i i i I 15.0 30.0 45.0 60.0 TIME (JULIAN DAY) (X10 ] ) 75.0 Figure 8 - Plots of s a l i n i t y versus time for five d i f f e r e n t points along the southern section (x=0,1/3,1/2,2/3,1) 32 m II x ct V 1980 1981 a o n ro -v. cm O ce } ! ( ! ( 0.0 15.0 30.0 45.0 60.0 75.0 TIME (JULIAN DAY) (X10 ] ) T 1 1 1 1 ° 0.0 15.0 30.0 45.0 60.0 75.0 TIME (JULIAN DAY) (X10 ] ) a ro a o o. ro ro x o I I 1 1 1 0.0 15.0 30.0 45.0 60.0 75.0 TIME (JULIAN DAY) (X10 ] ) 0.0 15.0 30.0 45.0 60.0 75.0 a . a __. ro cn o a TIME (JULIAN DAY) (X10 ] ) 1 1 1 1 1 0.0 15.0 30.0 45.0 60.0 75.0 TIME (JULIAN DAY) (X10 ] ) Figure 9 - Plots of s a l i n i t y versus time for five d i f f e r e n t points along the northern section (x=0,1/3,1/2,2/3,1) 33 map in F i g . 1 , t h i s is the only point where data were obtained close to a ferry terminal. When the ferry i s docked, the engines are kept running to position the fer r y . Held at a fixed position, the sea water coolant i s heated up and an increase in engine room temperature takes place. A corresponding increase in s a l i n i t y was measured by the instruments. In addition, i t was observed that s a l i n i t i e s were higher when the ferry was leaving compared with i t s a r r i v a l 20 minutes e a r l i e r . This i s most l i k e l y an a r t i f a c t of the heating in the engine room following the docking. In an e f f o r t to avoid contamination from thi s e f f e c t , i t was decided to look at data at one-third rather than at quaterly intervals along each section. Coming back to F i g . 9, one can see that for the northern section the discharge effect i s less apparent near Vancouver Island. This i s understandable since t h i s i s farthest from the Fraser River mouth. It i s interesting to notice that on the northern section during the anomalous discharge in December 1980 however, the s a l i n i t i e s at x= 1/3, 1/2 and 2/3 seem to be most affected, with the minimum s a l i n i t y around x=2/3. During the high summer discharges, the plume f i r s t a f f e c t s the s a l i n i t y at the point closest to the mainland and as the discharge increases, slowly advances towards Vancouver Island. This progression w i l l be c l e a r l y seen in the d a i l y variance to be discussed in the next subsection. 34 3.3 Comparison Of The Daily Variance Series In addition to causing a strong s a l i n i t y gradient (the front ) , high discharges should introduce more v a r i a b i l i t y in the estimate of s a l i n i t y at a point. Figs. 10 and 11 show the d a i l y variance of the s a l i n i t i e s at fixed points across the S t r a i t for the southern and northern sections, respectively. Most of the variance i s during periods of high discharge (Julian days 120 to 180, around day 361 and between Julian days 480 and 620). For the northern section, the i n t e r v a l of time over which the variance i s s i g n i f i c a n t , varies with position along the section. At x=1, the variance becomes s i g n i f i c a n t l y above 0 around Julian day 111. The time of t h i s change in variance progressively increases as x decreases to about Julian day 135 at x=0 near Vancouver Island. After the spring-summer discharge maximum, the plume retreats, ceasing to influence the s a l i n i t y at x=0 around Ju l i a n day 210. The same progression i s seen for the spring-summer 1981 discharge. The time l i m i t s of influence of the plume at x=1 are about from Julian days 480 to 620 while the analogous time l i m i t s at position x=0 are J u l i a n days 510 and 545. It seems to indicate that a discharge of 3000 m3/s and over i s needed to have the plume reach the northern section. This across s t r a i t progression i s not evidenced on the southern section. It might be because t h i s section is so close to the Fraser River mouth that the plume influences the whole section at the same time st a r t i n g around Julian days 110 and 495 for the spring discharges of 1980 and 1981, respectively. The large d a i l y variance at x=1 on the southern section i s probably 1980 1981 OQ II X o a (M O O \ o D.D a _. n CM II X L U (_> cr ct: c r a a O.D a _. OQ fM n x a a CE cn D.D a a . OQ • — i m cr ^ a x o 0.0 a __. oo ^ o il x a a O.D 1 T ~ — T 15.0 30.0 45.0 60 0 TIME (JULJflN DRY) (X10 ] ) i J 15.0 30.0 45.0 60 0 TIME (JULIRN DRY) (X10 3 ) 15.0 30.D 45.0 60 0 TIME (JULIRN DRY) (X10 ] ) 15.0 30.D 45.0 60 0 TIME (JULIRN DRY) (X10 ] ) i r 1 r 15.0 30.D 45.0 60 0 TIME (JULIRN DRY) (X10 ] ) 75.0 75.0 75.0 75.0 75.0 Figure 10 - Plots of the dai l y variance of s a l i n i t y versus time for five d i f f e r e n t points along the southern section (x=0,1/3,1/2,2/3,1) 1980 1981 ii X a a o o D .0 6 ^ •—• (M II X CJ ci CE cr a o I a 15.0 30.0 45 0 TIME (JULIAN DAY) (X10 3 60.0 ) 75.0 0.0 T II X a a 15.0 30.0 45 0 TIME (JULIAN DAY) (X10 ] 60.0 ) 75.0 CE CO D.O CD 15 0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 ] ) 75.0 CD II X a a 15 0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 3 ) 0.0 1 I •A-jK.. T15 0 30.0 45.0 60.0 TIME ( J U L I A N DAY) (X10 ] ) 75.0 Figure 11 - Plots of the da i l y variance of s a l i n i t y versus time for f i v e d i f f e r e n t points along the northern section (x=0,1/3,1/2,2/3,1) 37 partly due to the problem of the ferry docking previously described. It i s interesting to note that on the northern section, during the anomalous discharge of December 1980, the d a i l y s a l i n i t y variances at x=1/3, 1/2 and 2/3 seem to be the greatest while at the ends of the section they are r e l a t i v e l y low. 3.4 Combined Effects Of The Wind And Discharge On The Plume  Characteristics No obvious v i s u a l correlations could be found by comparing the time series of the wind with those of the plume c h a r a c t e r i s t i c s for the two year period as was done for the discharge in Figs. 6 and 7.. Some insight may be gained by analysing the e f f e c t of the wind during short intervals of time (20 to 30 days ), the order of the important wind fluctuation periods. Three intervals of time are examined; they also correspond to the cases for which extensive numerical modelling is described in chapter 5. The December Peak discharge i s given special attention and the two sharp increases in discharge in the springs w i l l be the subjects of the two other cases. 3.4.1 Spring 1980 This period i s characterized by an increasing discharge that leads to the general decreasing trend in the northern section s a l i n i t y (Fig. 12). Such a decreasing trend i s not evidenced in the southern section s a l i n i t y . After three days of variable wind (Julian days 119 to 122), three days of 38 ro Z O •—• o — ! \ CO ^_ 139.0 124.0 TIME 1 129.0 (JULIRN 134.0 DRY] 139.0 cn \ ro CD O O o ! ] 9 .0 CE CO I 124.0 TIME I 129.0 (JULIRN 1 134.0 DRY] 139.0 Figure 12 - Plot of the River discharge ( s o l i d l i n e , t o p ) , s t i c k diagram of wind (top), and plots of average s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d l i ne) and northern (broken line) sections vs time during the Spring 1980 northwesterly winds (Julian days 122 to 125) do not seem to have much e f f e c t on the plume c h a r a c t e r i s t i c s except an increase in the s a l i n i t y gradient on the southern section. On the other hand, the four following days (125 to 129) show the effect of southeasterly wind advection that brings the fresh water close 39 to the northern section and away from the southern section. Accordingly, the s a l i n i t y on the northern section i s seen to decrease while the s a l i n i t y on the other section i s seen to s i g n i f i c a n t l y increase. A peak in the s a l i n i t y gradient i s reached for the northern section while this c h a r a c t e r i s t i c on the southern section drops from the peak i t attained previously due to the negative along s t r a i t wind. Two days (129 to 131) of negative along s t r a i t wind that pushes the plume towards the southern section, are enough to cease the decrease of s a l i n i t y on the northern section and cause a drop in the southern section s a l i n i t y . It i s accompanied by an increase in s a l i n i t y gradient on that section while t h i s c h a r a c t e r i s t i c for the northern section drops from i t s highest value for that period, r e f l e c t i n g the mixing that eliminates the s a l i n i t y difference. A' return of southeasterly wind for the next three days (131 to 134) did not give r i s e to a s i g n i f i c a n t response on the northern section while the predicted r i s e of s a l i n i t y and drop of s a l i n i t y gradient are observed on the southern section. The drop of southern section s a l i n i t y and the increase of s a l i n i t y gradient, subsequent to t h i s event, might have been pa r t l y i n i t i a t e d by the northwesterly wind on day 135, but the stretch of positive along s t r a i t wind after that day should have brought the s a l i n i t y up again. The e f f e c t of the high discharge l e v e l at that time might have counteracted t h i s wind e f f e c t . The combined e f f e c t s of the wind and discharge helped decrease the s a l i n i t y at the northern section. 40 3.4.2 December Peak The signature of the discharge pattern i s c l e a r l y v i s i b l e in a l l four c h a r a c t e r i s t i c s shown in F i g . 13. The high discharge induced drops in average s a l i n i t y and sharp peaks in 356.0 361.0 366.0 371.0 376 0 TIME (JULIAN DAY) Figure 13 - Plot of the River discharge ( s o l i d l i n e , t o p ) , stick diagram of wind (top), and plots of average s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d line) and northern (broken l i n e ) sections vs time during the December Peak 41 the s a l i n i t y gradients. It i s seen in F i g . 13 that the high peak discharge occurs mainly during a period of positive wind (south-east) that should push the fresh plume water towards the northern section. This combination of wind and discharge i s responsible for the s a l i n i t y drop on the northern section at days 361-362, a time of only gradual s a l i n i t y decrease on the southern section. It i s only when, on day 364, the wind reverses di r e c t i o n that there i s a s i g n i f i c a n t s a l i n i t y drop on the southern section while the s a l i n i t y on the northern section is seen to increase. The magnitudes of the maximum gradient respond sharply to the discharge and the wind. They also show the delay in the response of the southern section in comparison to the response of the northern section. After the discharge disturbance i s over, the s a l i n i t i e s and the s a l i n i t y gradients slowly go back to the l e v e l they were at before the event. 3.4.3 Spring 1981 As for the spring 1980 case, the discharge i s progressively increasing throughout the i n t e r v a l of time studied (Fig. 14). The general decreasing trend of the s a l i n i t y on the northern section, supported by the gradual increase of s a l i n i t y gradient shows the o v e r a l l freshening e f f e c t of the discharge. On the other hand, the large increase of the southern section s a l i n i t y between J u l i a n days 516 and 524 can not be discharge-related. A look at the wind record i d e n t i f i e s the cause of the s a l i n i t y increase as being high southerly winds that take the plume away from the southern section, reducing at the same time the 42 (_)<=> <=> Figure 14 - Plot of the River discharge ( s o l i d l i n e , t o p ) , s t i c k diagram of wind (top), and plots of average s a l i n i t i e s (middle) and s a l i n i t y gradients (bottom) for the southern ( s o l i d l i ne) and northern (broken line) sections vs time during the Spring 1981 s a l i n i t y gradient. Low s a l i n i t i e s and high gradients are encountered on the southern section during a combination of high discharge and northwesterly winds (Julian days 512 to 516). The burst of negative wind on day 512 might be responsible for the peak in the northern section s a l i n i t y on that day accompanied by 43 a s l i g h t decrease of s a l i n i t y gradient magnitude. The long stretch of posit i v e wind between Julian days 501 and 512 i s ce r t a i n l y responsible for the s a l i n i t y v a r i a t i o n on the southern section from days 501 to 508. On that day (508), due to a weakening of the wind or to a greater importance of the discharge, s a l i n i t y starts to drop and the s a l i n i t y gradient to r i s e . During the period from Julian days 498 to 501, low s a l i n i t i e s and r e l a t i v e l y high gradients of s a l i n i t y on the southern section were maintained by negative winds pushing the plume towards that section while high s a l i n i t i e s were found on the northern section. The analysis of these three cases i s e f f e c t i v e in showing the effects of the wind in producing variations of the plume c h a r a c t e r i s t i c s . While these effects have been predicted by many workers (Feely and Lamb, 1979; Duffus and T i l l e y , 1978; Stronach, 1981), the ferry data provides the f i r s t set of time series which allow this assumption to be v e r i f i e d . 44 IV. STATISTICAL ANALYSIS 4.1 Cross-correlations Cross-correlations can be used as a tool to quantify the suspected r e l a t i o n between the forcing parameters (wind and discharge) and the plume c h a r a c t e r i s t i c s (average s a l i n i t y and magnitude of the maximum s a l i n i t y gradient). Table V summarizes the cross-correlation computations for the longest possible d a i l y series (three series per section). The computations were performed with the plume c h a r a c t e r i s t i c and the forcing parameter in such an order so as to give a peak in the cor r e l a t i o n function at a negative lag when the forcing parameter i s leading the plume c h a r a c t e r i s t i c fluctuations. The peak correlations were tabulated along with the corresponding time lags. If two s i g n i f i c a n t peaks are present in the cross-c o r r e l a t i o n function, they are both written in Table V. 4.1.1 Discharge As can be seen from Table V, the time lags in the discharge correlations are negative (or 0.) indicating that the discharge leads the variations of the plume c h a r a c t e r i s t i c s . The exact value of the lag (fluctuates between -7 and 0 days) i s , however, not s t a t i s t i c a l l y s i g n i f i c a n t at the 99 % l e v e l and i s seen to vary from one data period to the other for the same section. This conclusion of non-significant differences between the di f f e r e n t data periods also holds for the corr e l a t i o n c o e f f i c i e n t s . The correlations themselves are f a i r l y high and 45 Table V - Results of the cross-correlation computations between the plume c h a r a c t e r i s t i c s and the forcing parameters Discharge Along-strait wind component Cross- Day Cross- Day corr e l a t i o n lag correlation lag c o e f f i c i e n t c o e f f i c i e n t AVERAGE SALINITY Southern section Julian days: 80-327 -0.65 -1 0.42 -1 352-541 -0.69 -4 0.40 5 570-680 -0.37 -3 0.56 -2 Northern section Julian days: 52-273 -0.87 -7 -0.18 -4 325-416 -0.86 -2 -0.19 -4 0.33 2 448-71 5 -0.83 0 0.24 6 MAGNITUDE OF THE MAXIMUM GRADIENT Southern section Julian days: 80-327 0.43 -1 -0.18 -1 352-541 no s i g . no s i g . cor r e l a t i o n c o r r e l a t i o n 570-680 0.42 -2 -0.42 -2 Northern section Julian days: 52-273 0.59 -1 0.17 -2 -0.19 2 325-416 0.67 -2 0.34 -3 -0.30 2 448-715 0.64 0 -0.25 1 3 si g n i f i c a n t at the 99 % l e v e l except for the magnitude of the s a l i n i t y gradient on the southern section during the Julian day period 352-541. The correlations are suprisingly higher on the 46 northern section than on the southern section for both plume c h a r a c t e r i s t i c s . This might be due to the C o r i o l i s force which could favor the northern section by deflecting fresh water towards i t . Also, the southern section i s closer to the input of salty ocean water through the S t r a i t of Juan de Fuca. The northern section, however, i s f a i r l y well removed from any strong sources of sea water. Thus, some of the fluctuations at the southern section, may be responses to variations in sea water input and be unrelated to changes in river discharge. A lower correlation with the magnitude of the maximum gradient than with the average s a l i n i t y was expected because the former i s not continuous. For example, on the southern section, at high discharge, the front can go beyond x=0, through a pass (Fig. 1) so that the gradients on the section i t s e l f are low. The sign of the corr e l a t i o n indicates that, as expected low s a l i n i t i e s and high gradients are related to and follow high discharges as seen in the time series of chapter 3. 4.1.2 Wind Unlike the discharge corr e l a t i o n s , the wind cross-c o r r e l a t i o n c o e f f i c i e n t s and time lags fluctuate greatly from one time period to another for a pa r t i c u l a r plume c h a r a c t e r i s t i c . This i s a f i r s t hint at the ef f e c t that the wind causes s a l i n i t y variations that are not independent of the general water properties and discharge l e v e l present at the time. The along-strait wind component i s only weakly correlated 47 (table V) with the plume c h a r a c t e r i s t i c s . In t h i s case, positive time lags are nearly as frequent as negatives ones. They occur in such a way that a quadrature re l a t i o n s h i p between the forcing parameter and the plume c h a r a c t e r i s t i c is suspected. Cross-spectra between those two parameters constitute a better tool to investigate the phase difference between the two series. The c o r r e l a t i o n c o e f f i c i e n t s with the wind are low but are s t i l l s i g n i f i c a n t at the 99 % l e v e l . The effect of the wind i s more strongly f e l t at the southern section than at the other section. This is in contrast to the effects of the discharge on the two sections. If we think of positive along-strait winds as advecting the fresh water of the plume towards the northern section then, for strong positive winds, high s a l i n i t i e s can be expected at the southern section and low s a l i n i t i e s at the northern section. Thus, a p o s i t i v e c o r r e l a t i o n of the average s a l i n i t y on the southern section with the along-strait wind component and a negative correlation with the same ch a r a c t e r i s t i c on the northern section are expected. Moreover, i f the proximity of the plume to a section increases the s a l i n i t y gradient then high gradients on the southern section should be seen when the plume i s advected towards th i s section i . e . with a negative along-strait wind component. This process predicts a negative c o r r e l a t i o n between the magnitude of the maximum gradient on the southern section with the along-strait wind component and a p o s i t i v e one on the northern section. These assertions regarding the signs of the correlations for the southern section plume c h a r a c t e r i s t i c s are v e r i f i e d as can be 48 seen from table V but the quadrature property of the relationship between the northern section c h a r a c t e r i s t i c and the wind parameter do not allow any statements about the phase u n t i l cross-spectra are computed. 4.2 Linear And Non-linear Combination Of The Wind And Discharge In t h i s section, an attempt w i l l be made to state how much of the variations of the average s a l i n i t y and the magnitude of the maximum gradient can be explained by a lin e a r combination of the wind and the discharge parameters. If such a combination of wind and discharge i s found to describe reasonably well the ferry data, i t could then be used to interpolate during periods of missing data and to extrapolate for other years. The notation w i l l follow e s s e n t i a l l y that of Jenkins and Watts (1968). Let's suppose that the detrended output X (that t3 w i l l be either the average s a l i n i t y or the s a l i n i t y gradient) can be written as: X = h,X + h 2X + Z t3 ( t - r ) l (t-s)2 t for t = 1,2...N 3.1 where h, and h 2 are linear c o e f f i c i e n t s , r i s the lag time of the effect of the series X (that t1 w i l l be the discharge series) on the output X , t3 s i s the lag time of the ef f e c t of the series x (that t2 w i l l be the along-strait wind component series) on the output X , t3 49 Z i s a noise term that w i l l be assumed to be white, t The previous equation can be written in matrix form: x = Xh + Z 3.2 where X = h' = (h, h 2) x x ( l - r ) l ( 1 - S ) 2 x x (N-r)l (N-s)2 x' = (x x ...x ) 13 2 3 N 3 Z' = (z z . . .z ) 1 2 N By multiplying the matrix equation by X ' / N , one gets: ( 1 / N ) X ' X = ( l / N ) ( X ' X ) h + ( 1 / N ) X ' Z . 3.3 Each element of the matrix ( 1 / N ) X ' Z i s a cross-covariance estimate between the inputs and the noise. This i s e s s e n t i a l l y zero. The matrix ( 1 / N ) X ' X can be rewritten in terms of the cross-correlation c o e f f i c i e n t matrix of the inputs: N ( ( 1 / N ) X ' X ) , , = ( 1 / N ) L x x k=1 ( k - r ) 1 ( k - r ) l = VAR(X,) f N ( ( 1 / N ) X ' X ) 2 2 = ( 1 / N ) L x x k=1 ( k - s ) 2 ( k - s ) 2 = VAR(X 2), 50 N ( ( 1 / N ) X ' X ) 1 2 = ( ( 1 / N ) X ' X ) 2 1 = (1/N) L x x k=1 ( k - r ) l (k-s)2 1/2 = r ! 2 ( r - s ) ( V A R ( X , ) V A R ( X 2 ) ) 3.4 where r 1 2 ( r - s ) i s the cross-correlation c o e f f i c i e n t at lag (r-s) between time series 1 and 2. The matrix ( 1 / N ) X ' X can be written in terms of the cross-correlation c o e f f i c i e n t s between the inputs and the output: N ( ( 1 / N ) X ' X ) , , = (1/N) L x x k=1 (k - r ) l k3 1/2 = r , 3 ( r ) ( V A R ( X , ) V A R ( X 3 ) ) N ( ( 1 / N ) X ' X ) 2 1 = (1/N) I x x k=1 (k-s)2 k3 1/2 = r 2 3 ( s ) ( V A R ( X 2 ) V A R ( X 3 ) ) . 3.5 F i n a l l y the matrix equation can be rewritten and solved for h, and h 2 . The results are 1/2 r , 2 ( r - s ) r 2 3 ( s ) - r , 3 ( r ) h, = ( V A R ( X 3 ) V A R ( X , ) ) r ? 2 ( r - s ) - 1 1/2 r ! 2 ( r - s ) r , 3 ( r ) - r 2 3 ( s ) h 2 = ( V A R ( X 3 ) V A R ( X 2 ) ) . 3.6 r ? 2 ( r - s ) - 1 The linear combination should attempt to describe the data as a whole and not only small sections of i t . The various estimates of cross-correlation c o e f f i c i e n t s and variances needed to compute h, and h 2, should characterize the s t a t i s t i c s of both years of data. In view of the uniformity of the cross-c o r r e l a t i o n c o e f f i c i e n t s of Table V and the i n s i g n i f i c a n t 51 variations of the time lag for d i f f e r e n t time periods for a pa r t i c u l a r section and plume c h a r a c t e r i s t i c , an arithmetic average of the three (two in the case of the southern section s a l i n i t y gradient) cross-correlation c o e f f i c i e n t s should give the desired estimates for r 1 3 and r 2 3 . In cases where two cross-correlation c o e f f i c i e n t s at di f f e r e n t time lags are discussed, the highest one of the two i s used in the computation of the averaged cross-correlation c o e f f i c i e n t s . These are given in Table VI and they exhibit the same general properties described in the previous section concerning the size and the Table VI - Averaged cross-correlation c o e f f i c i e n t s between the plume c h a r a c t e r i s t i c (Series 3), the discharge (Series 1), the wind (Series 2) and the linear combination (Series 4) C 1 3 r r 2 3 s r« 3 r 2 r 3 1 2 AVERAGE SALINITY Southern section -0.57 1 0.46 1 0.66 47 % Northern section -0.85 2 0.13 0 0.88 72 % MAGNITUDE OF THE MAXIMUM GRADIENT Southern section 0.43 1 -0.3 0 0.47 25 % Northern section 0.63 2 -0.03 2 0.63 40 % sign of the values of the correlations for the d i f f e r e n t plume c h a r a c t e r i s t i c s . The values of r 2 3 are low and i n s i g n i f i c a n t for the northern section c h a r a c t e r i s t i c s and also carry the opposite sign to that predicted by wind advection. The cross-c o r r e l a t i o n between discharge and wind ( r 1 2 ) produced a uniform value of -0.13 around 0 day lag. This value i s very low and not s i g n i f i c a n t as expected. The time lags r and s associated with 52 the average cross-correlation estimates of Table VI were obtained by finding the combination of r and s that gives the highest cross-correlation at lag 0 between the plume c h a r a c t e r i s t i c data and the linear combination. The values of the l a t t e r cross-correlation c o e f f i c i e n t s (r„ 3) are shown in Table VI along with the percentage of the data series variance explained by the linear combination, a value also known as the multiple c o r r e l a t i o n c o e f f i c i e n t ( 1 ^ 3 1 2 ) . The multiple c o r r e l a t i o n c o e f f i c i e n t i s expressed as follows: r i i 2 = ( r ? 3 + r | 3 " 2 r , 2 r , 3 r 2 3 ) / ( 1 - r ? 2 ) . 3.7 The conclusions to be drawn from these correlations are that in general the co r r e l a t i o n i s better between the data and the linear combination than with the two forcing parameters separately, and that the average s a l i n i t y i s a better c h a r a c t e r i s t i c compared to the s a l i n i t y gradient to see the influence of wind and discharge. A reconstruction of the plume c h a r a c t e r i s t i c series from the detrended output of the linear combination i s shown in Figs. 15 and 16. This reconstruction used the slopes and intercepts from the e a r l i e r detrending procedure done on the plume c h a r a c t e r i s t i c s . The detrending procedure yielded a value of 0 for the slopes and of 24.7 0 / 0 0 for the average s a l i n i t y intercepts. Intercept values for the s a l i n i t y gradient trends are 1.3 and 1 (o/oo)/km for the southern and northern sections, respectively. These linear reconstructions (Fig. 15 b,d and 16 b,d) show a lack of fluctuations compared to the data series of Fig.15 a,c and 16 a,c. A large portion of the variance (in most of the cases, 53 1980 1981 fl) B) C) D) O O cr Q a I o D .0 a _ n O O a a D . 0 a S i i—i o a o cr ^ CrT O a CD ~ • • D .0 C E O CO ° o -rn' a 0 .0 ~i 1 1 1 — 15.0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 ] ) n i 1 1 — 15.0 30.0 45.0 60 0 TIME (JULIAN DAY] (X10 ] ) ' n i 1 1 — 15.0 30.0 45.0 60 0 TIME (JULIAN DAY) i X \ 0 ] ) 15.0 TIME 1 30.0 (JULIAN 1 1 — 45.0 60.0 DAY) (X10 3 ) ~1 75.0 ~1 75.0 75.0 75.0 Figure 15 - Plots of northern section plume c h a r a c t e r i s t i c s versus time: a) average s a l i n i t y ferry data, b) average s a l i n i t y from li n e a r combination, c) maximum s a l i n i t y gradient ferry data, d) maximum s a l i n i t y gradient from linear combination 54 1980 1981 BJ C) D) o . tn O O O a a CT CO a _ tn O O a a D.O o I— ^ L n ' ' I—H O a o . cr \ • OH O a CD ^ -_• • 2 ^ a cr o co o O c , i l n 1 — 1 1 5 - ° T 30.0 45.0 60 0 TIME (JULIAN DAY) ( X J 0 ] ) ' 0.0 ~1 75.0 T 15 0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 3 ) 75.0 "i r D-° 15.0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 3 ) 75.0 ^ ^ ^ ^ T 1 T 15 0 30.0 45.0 60 0 TIME (JULIAN DAY) (X10 ] ) ' 75.0 Figure 16 - Plots of southern section plume c h a r a c t e r i s t i c s versus time: a) average s a l i n i t y ferry data, b) average s a l i n i t y from linear combination, c) maximum s a l i n i t y gradient ferry data, d) maximum s a l i n i t y gradient from linear combination 55 more than 50 %, Table VI) i s s t i l l unexplained by the wind and the discharge or cannot f i t into the l i n e a r i t y assumption of the combination of the two forcing parameters. In view of the increased v a r i a b i l i t y of the plume c h a r a c t e r i s t i c s during high discharge (Fig. 6 and 7), i t was thought that a better combination of the wind and the discharge would be to make the contribution due to the wind (h 2X ) t2 dependent on the discharge by multiplying i t by a factor of the form C exp(kX ) where X has units of 103 m3/s. By (t-r)1 ( t - r ) l slowly varying the value of k and finding the corresponding value of C that minimized the squared differences between the resulting combination and the average s a l i n i t y data, sets of two number (k and C) were found that maximized the correlations between the non-linear combination and the ferry data. The optimized k values were 0.4 and 0.6 for the southern and northern sections, respectively. The res u l t i n g cross-correlations for the non-linear combination were s l i g h t l y above the corresponding correlations for the linear combinations. No improvement in the v a r i a b i l i t y in the reconstructed series from the non-linear combination of wind and discharge was found and this r e f l e c t e d the ef f e c t of the optimization procedure in trying to minimize the wind contributions (the optimized values of C were quite low). By a r b i t r a r i l y increasing the value of C by a factor of 3 for the non-linear combination of the southern section average s a l i n i t y , the resultant series (Fig 17 b) shows a better q u a l i t a t i v e agreement of the v a r i a b i l i t y l e v e l between 56 1980 1981 R) B) ro O O O a a CE CO 0 .0 Q — , O O O o a 0 .0 T 15.0 TIME T 30.0 45.0 (JULIRN DAY) (X10 ] 60.0 ) 75.0 ^ ^ ^ ^ ~1 15.0 TIME 1 1 1 — 30.0 45.0 60.0 (JULIRN DRY) (X10 3 ) 75.0 Figure 17 - Plots of the average s a l i n i t y versus time for the a) northern and b) southern sections as given by a non-linear combination of wind and discharge the combination and the data. Nevertheless, i t i s accompanied with a s l i g h t decrease in the actual cross-correlation c o e f f i c i e n t (0.62). When the value of C for the combination resulting in the estimation of the northern section s a l i n i t y , i s optimized with k=0.4, C becomes negative and increases by a factor of 14 compared to the optimized C value with k=0.6. This d i f f e r e n t set of k and C e f f e c t i v e l y increases the wind contribution to a l e v e l that improves the q u a l i t a t i v e accord between the combination series and the data (Fig. 17 a). The cross-correlation computation quantifies t h i s accord to a value of 0.80. The fact that the constant C i s now negative brings 57 the sign of the wind contribution in agreement with the effect of wind advection for s a l i n i t y near the northern section. 4.3 Spectra And Cross-spectra In an attempt to achieve maximum spectral resolution and use the f u l l length of the data as a single time series, the gaps between the three d a i l y series for each plume ch a r a c t e r i s t i c and each section were f i l l e d with the appropriately reconstructed linear combination of the wind and the discharge described in the previous section. It was f e l t that the time intervals covered by these gaps were small compared to the t o t a l length so that they would not modify the spectral r e s u l t s . To support t h i s assumption, an o v e r a l l comparison between the spectral results from the three d i f f e r e n t portions of the data record and the results from the f u l l data record did not show any major differences. Spectra of the daily forcing parameters and the plume c h a r a c t e r i s t i c s are displayed in Fig 18. The major contributions to the spectrum of the discharge are at periods longer than 20 days while the periods of the wind fluctuations are mostly shorter than 20 days with a sharp peak at 6 days and a broad one between 10 and 20 days. This nicely separates the possible effects of the discharge from those of the wind in frequency space. Looking now at the spectra of the plume c h a r a c t e r i s t i c s , one sees that only the spectrum of the northern section average s a l i n i t y c l e a r l y appears red similar to the discharge spectrum. Peaks at 6 days for the southern section 58 LU CJ ac cr BJ DISCHARGE CJ LU oc a |H 11 I I I—I [IIM I I I I [Mil I | |—| 1 ID3 JO1 JQ< JO* LOG(PERIQD) IDRTJ SOUTHERN SECTION AVERAGE 5ALINITY a LU oc X oc LU a J£P LU^" CJ " Z CE. oc cr a LU oc u_ MC OC LU a mn i i i |i>11 I I I I [mii i i i 1 JO' ]0- JO* LOGtPERJODJ (DRY! SOUTHERN SECTION SflLJNJTY BRADI ENT Q (III I I I I—| [Mil I I I—I [Mill I I I 1 JO 3 JO* 10' JO* LOG(PERIOD) tDBTJ LU U cr > a LU DC Lu DC LU 3 a ALONG-5TRAIT WIND DJ a | t n n - n i | i in 11 i—i f t n r m — i 1 JO* JO* JO' JO* LOG (PERIOD) (DRY) LU CJ 2 1 cr DC cr NORTHERN SECTION AVERAGE SALINITY FJ j "ium i i—i—11111 I I I I — 1 1 1 1 1 1 1 1 — i — | JO* JO' JO- JO* LOG (PERIOD) (DRYJ LU CJ cr »—i c t cr a LU oc U_ OC a NORTHERN SECTION SALINITY GRADIENT "1"" " M l |IHI I I I 1 | l l l l l I I I j I F JO* J0 J i0* LOG(PERIOD) (DRY! Figure 18 - Plots of normalized spectra of a)the Fraser River discharge, b) the along-strait wind component, c)the southern and d) northern section average s a l i n i t i e s and the e) southern and f) northern section maximum s a l i n i t y gradient 59 spectral estimates and the broad peak over the period i n t e r v a l of 10 to 20 days for a l l c h a r a c t e r i s t i c s (except the northern section s a l i n i t y spectrum) are quite similar to the corresponding peaks in the wind spectrum. To quantify t h i s s i m i l a r i t y between the spectral representation of the forcing parameters with the plume c h a r a c t e r i s t i c s , cross-spectra have been computed and the peaks in coherency are tabulated in Tables VII and VIII. 4.3.1 Cross-spectra With The Discharge One should notice that in the cross-spectra of Table VII, the highest squared coherency occured at the lowest computed Table VII - Results of the cross-spectra between the plume ch a r a c t e r i s t i c s and the ri v e r discharge Maximum Squared Coherency Corresponding Period (days) Phase lag AVERAGE SALINITY Southern section 0.82 149 179°± 8° Northern section 0.92 165 -171°± 2° MAGNITUDE OF THE MAXIMUM GRADIENT .Southern section Northern section 0.50 0.87 149 165 -20°±20° 0°± 4° frequency. This frequency depends on the length of the record and the averaging taper. The values of the squared coherency are high, except for that of the southern section s a l i n i t y gradient and are above the noise l e v e l for periods over 30 days. The order, of importance of the maximum coherency follows the 60 same order as the cross-correlation c o e f f i c i e n t s ( r 1 3 ) of Table VI: higher coherencies found with the northern section c h a r a c t e r i s t i c s than with the southern ones and a more coherent r e l a t i o n between the average s a l i n i t i e s and the discharge than between the s a l i n i t y gradients and the discharge. The phases of Table VII also agree with the signs of the correlations given in Table VI. The uncertainties in the phases are taken from F i g . 9.3 of Jenkins and Watts (1968). An exact lag value (to the closest day) of the ef f e c t of the discharge on the plume c h a r a c t e r i s t i c s cannot be determined. It i s only in the case of the northern section s a l i n i t y that a tendency of the discharge to lead t h i s plume c h a r a c t e r i s t i c by a few days i s found. 4.3.2 Cross-spectra With The Wind As suggested above, one may be able to i d e n t i f y the small peaks in the spectra of the c h a r a c t e r i s t i c s (for periods below 20 days ) as possible wind e f f e c t s . Cross-spectra of the plume c h a r a c t e r i s t i c s with the along s t r a i t wind component were computed (Table VIII). This type of computation shows a weak but s i g n i f i c a n t coherence for the wind not only with the southern section plume c h a r a c t e r i s t i c s but also with the northern section. The peaks in coherence occur at d i f f e r e n t frequencies for each section. The sharp peak at 6 days in the wind spectrum appeared to influence the southern section cross-spectra but not those for the northern section. On the other hand, the broad peak between 10 and 20 days seemed to influence fluctuations of a l l four c h a r a c t e r i s t i c s . As expected from the 61 Table VIII - Results of the cross-spectra between the plume c h a r a c t e r i s t i c s and the along s t r a i t wind component Maximum Corresponding Phase Squared Period lag Coherency (days) AVERAGE SALINITY Southern section 0.63 6 60°±20° 0.51 19 -20°±20° Northern section 0.31 10 -30°±30° 0.31 12 -90°±30° MAGNITUDE OF THE MAXIMUM GRADIENT Southern section 0.34 6 -110°±30° 0.41 19 -170°±20° Northern section 0.46 12 140°±20° shape of the spectra, the worst cor r e l a t i o n with the wind was for the northern section s a l i n i t y . The phase differences for the average s a l i n i t i e s and magnitudes of the maximum gradients for each section at corresponding periods i s close to 180° indicating an out of phase rela t i o n s h i p between the two plume c h a r a c t e r i s t i c s on each section. Numerous phase values are close to the quadrature values of 90° or -90°. This could be explained as follow. Let's assume the along-strait wind component to be a sinusoidal function of either 6 or 12 days (periods corresponding to the periods of highest coherencies in the cross-spectra). One can think of t h i s along-strait wind component as advecting the body of fresh water as a whole in the same di r e c t i o n as the wind. During the posi t i v e part of the cycle, the water i s advected to the north so the southern section s a l i n i t y i s progressively increasing (while i t i s decreasing on the northern section) u n t i l the wind changes 62 dir e c t i o n and brings the fresh water back towards the southern section. Under these conditions, the s a l i n i t y maximum on the southern section should occur when the wind i s zero and changing from a posit i v e wind component to a negative one. The preceding explanation predicts a phase lag of 90° between the southern section average s a l i n i t y and the wind component and -90° between the northern section s a l i n i t y and the wind. The computed phases of 60° and -90° are not far from the expected phase lags. 4.4 Harmonic Analysis In order to evaluate fluctuations at t i d a l frequencies the average s a l i n i t y series were divided into two portions: the 1980 data and the data for 1981. Each portion was harmonically analysed and only the constituents l i s t e d in Table III were given special attention since they are the only constituents simultaneously monitored, by two f e r r i e s on the same section. The l i s t of constituents to receive attention i s further reduced by eliminating the constituents for which the amplitude does not exceed the noise l e v e l of 0.5 o/oo for the yearly harmonic analysis. Table IX summarizes the harmonic analysis for these constituents for the two years of data. Two constituents (Ssa and Mf) that could not be resolved in the analysis leading to Table II I , have been added to the l i s t . They both respect the c r i t e r a of having amplitudes above the noise l e v e l . If one excludes the results of S 2 for the southern section for which amplitudes are below the noise l e v e l and the difference between the phases of the two di f f e r e n t years i s 115°, no s i g n i f i c a n t 63 difference between the phases for the d i f f e r e n t years is noticed. The highest phase difference is 56° and i s lower than the fluctuation of the phases noticed to occur between two series obtained by two f e r r i e s on the same section (64°). On the other hand, the amplitudes of the fluctuations vary from one year to another. Small t i d a l amplitudes for the northern section are usually found in comparison to the corresponding amplitudes for the southern section. The proximity of the r i v e r mouth to the southern section, that leads in general to the presence of high horizontal s a l i n i t y gradients, might be responsible for this Table IX - Amplitudes (A) in o/oo and phases (0) from the harmonic analysis done on the average s a l i n i t y series for the two years of the data Southern section Northern section 1980 1981 1980 1981 A <P A <t> A <S> A <S> SSa 1 .7 46° 3.1 32° 3.4 53° 2.3 52° MSf 0.5 -26° 1.9 3° 0.2 -52° 0.4 -108° Mf 0.5 1 28° 1 .5 1 27° 0.2 65° 0.3 105° Pi 1 .5 -17° 0.6 0° 1 . 1 18° 1 .0 35° Ki 1 .7 18° 0.7 2° 1 .2 56° 1 .0 53° M2 0.6 -27° 0.4 -19° 0.0 180° 0.1 126° s 2 0.3 168° 0.1 -77° 0.5 -167° 0.4 -127° difference between the two sections. Stronger t i d a l currents near the southern section than near the northern section, have also been measured (Data Record of Current Observations, 1969-1970) and might be responsible for high t i d a l s a l i n i t y fluctuations on that section. The high amplitude of the Ssa •64 c o n s t i t u e n t , which has a h a l f - y e a r p e r i o d , can h a r d l y be r e l a t e d to the almost n e g l i g i b l e corresponding c o n s t i t u e n t i n the sea l e v e l e l e v a t i o n . The f a c t that the frequency of t h i s c o n s t i t u e n t l i e s w i t h i n the frequency band of the d i s c h a r g e , suggested that the l a r g e amplitudes at t h i s t i d a l frequency may be due to a discharge e f f e c t . I t i s not as c l e a r f o r the MSf and Mf c o n s t i t u e n t s that happen t o have f r e q u e n c i e s i n the range of the s p e c t r a l peaks of the wind. One can h a r d l y separate the e f f e c t s of the two f o r c i n g mechanisms, but some h i n t s favor the wind as the primary f o r c i n g . F i r s t , the northern s e c t i o n t i d a l amplitudes f o r these c o n s t i t u e n t s are not above the noise l e v e l . Secondly, the phases of the amplitudes of the southern s e c t i o n f l u c t u a t i o n s vary widely from MSf to MF. Both years i n d i c a t e t h a t f o r hig h f r e q u e n c i e s t i d a l c o n s t i t u e n t s ( d i u r n a l and s e m i - d i u r n a l c o n s t i t u e n t s ) and M 2 are the major c o n s t i t u e n t s f o r the southern s e c t i o n s a l i n i t y . On the northern s e c t i o n , i s again a major c o n s t i t u e n t but M 2 no longer i s , and i s even below the noise l e v e l . T h i s i s s u r p r i s i n g s i n c e the t i d e s i n the S t r a i t are c l a s s i f i e d as of the mixed dominantly s e m i - d i u r n a l type (Crean, 1976). The hig h frequency c o n s t i t u e n t phases f o r the average s a l i n i t y on the southern s e c t i o n are c l o s e to 0° or at l e a s t between -90° and 90° except i n the case of the S 2 c o n s t i t u e n t that has an amplitude below the noise l e v e l . Two processes might be invoked to e x p l a i n a r e l a t i o n between the t i d e s and the s a l i n i t y v a r i a t i o n s : the advection of the plume by the u n d e r l y i n g water and the modulation of the d i s c h a r g e . I t i s known (Crean, 1976) 65 that from the ebb- to the flood-tide, the water i s moving towards the northwestern part of the S t r a i t of Georgia and, conversely, to the southeast from high to low tides. Another e f f e c t of the tides i s the modulation of the r i v e r discharge. This occurs by changing the heights of the water in the r i v e r and in the S t r a i t . High discharges can occur at low tides while the r i v e r i s e f f e c t i v e l y shut off at high tides. Both processes (the advection of the plume and the modulation of the discharge) bring fresh water (thus lower s a l i n i t y ) to the southern section at low tides. This may be why the phases indicate an in-phase rela t i o n s h i p between the average s a l i n i t y on the southern section and the sea l e v e l elevation at Point Atkinson. On the northern section, the two processes act against each other. This leads to a more confused picture. As a consequence, there is no clear cut pattern in the phases relationship recorded that would favor an out-of-phase or an in-phase r e l a t i o n between the t i d a l forcing and the s a l i n i t y fluctuations. When the same analysis i s c a r r i e d out for the magnitude of the maximum gradient series, remembering that MSf was the only constituent for which the analysis done in chapter 2 l e f t some hope of being useful, i t turned out that for the yearly analysis none of the amplitudes of the MSf constituent were above the noise l e v e l . By examining the harmonic results at t i d a l frequency that could not be resolved in the analysis of section 1.3.4, only the SSa constituent acquires amplitudes above the noise l e v e l . The phases for that constituent are e s s e n t i a l l y i d e n t i c a l for both years and have a difference of 180° with the 66 phases recorded f o r the SSa s a l i n i t y f l u c t u a t i o n s . As mentionned before, the d i s c h a r g e more than the t i d e s seems to be the f o r c i n g mechanism r e s p o n s i b l e f o r f l u c t u a t i o n s at the SSa frequency. When harmonic a n a l y s i s i s performed on y e a r l y f r o n t a l s a l i n i t y g r a d i e n t s e r i e s , none of the c o n s t i t u e n t amplitudes are above the noise l e v e l . The only s i g n i f i c a n t amplitudes are o b t a i n e d by the y e a r l y a n a l y s i s of the f r o n t a l p o s i t i o n . I t o ccurs at the MSf frequency f o r the 1981 northern s e c t i o n s e r i e s . The phase computed i s 182°. The same problem of t h i s c o n s t i t u e n t being at a frequency of a wind peak i s s t i l l present but r e g a r d l e s s of the mechanism ca u s i n g the f l u c t u a t i o n , the phase i n d i c a t e s that the f r o n t a l p o s i t i o n i s n e a r l y i n phase with the s a l i n i t y (182° compared to -108°, (Table I X ) ) ; that i s , low s a l i n i t i e s on the northern s e c t i o n are recorded when the plume f r o n t i s near Vancouver I s l a n d . The f r o n t a l p o s i t i o n and the s a l i n i t y are i n phase on the southern s e c t i o n even though the amplitudes of the MSf f l u c t u a t i o n s i n p o s i t i o n are below the n o i s e l e v e l . As f o r the wind, i t i s suggested that the amplitudes of the induced t i d a l f l u c t u a t i o n s might depend on the s t r e n g t h of the r i v e r d i s c h a r g e . To i n v e s t i g a t e t h i s assumption, the data r e c o r d was separated i n t o nine p o r t i o n s , d i v i d e d so that each p o r t i o n i s c h a r a c t e r i z e d by a c e r t a i n l e v e l of d i s c h a r g e . P o r t i o n s of the r e c o r d d u r i n g which the d i s c h a r g e i s between 0 and 3000 m 3/s are c h a r a c t e r i z e d by a low d i s c h a r g e ( L ) . T h i s o c c u r s f o r data p o r t i o n s 1,4,6 and 9 c o v e r i n g i n terms of J u l i a n 67 Figure 19 - Northern (top) and southern (bottom) section s a l i n i t y fluctuation amplitudes for the K, ( s o l i d line) and M2 (broken l i n e ) constituents from harmonic analyses done on nine d i f f e r e n t data portions characterized by a discharge l e v e l (L,M,H) 68 days the periods 52 to 109, 283 to 353, 373 to 479 and 618 to 669. Records with discharge between 3000 and 5000 m3/s are coded as medium discharge portions (M). Data portion 3 and 8 are characterized by t h i s type of discharge. They correspond to periods between Julian days 206 and 282 and also 583 and 617. F i n a l l y , when the discharge is over 5000 m3/s, the portions of the data are associated with high discharge (H). These are data portions 2,5 and 7 with corresponding Julian day periods: 121-205, 354-372 and 504-582. Harmonic analyses have been performed on each of the nine individual portions of the average s a l i n i t y record for each section. The comparison between the amplitudes of the K, and M2 constituents for the nine portions of data i s displayed in F i g . 19. The l e t t e r s on the x-axes correspond to the l e v e l of the discharge during that portion. Series 5 corresponds to the anomalous December Peak. Fi g . 19 c l e a r l y shows the dominance of K, over M2 for both sections. It also shows that the northern section amplitudes are rarely above the noise l e v e l (0.5 o/oo) and because of that do not show any d e f i n i t e r e l a t i o n with the l e v e l of the discharge. On the other hand, the southern section amplitudes, while being in general above the noise l e v e l , reproduce the pattern of the discharge l e v e l for both constituents. Low discharges correspond to amplitude minima and high discharges to amplitude maxima. The only exception i s the.K, amplitude of series 4 that exhibits an anomalous high value for a low discharge l e v e l . 69 V. COMPUTER SIMULATIONS 5.1 Description Of An Existing Model Of The Fraser River Plume Stronach (1977) developed a numerical model of the thin layer of the Fraser River Plume. It i s worthwhile to go over the p r i n c i p l e s and equations on which that numerical model i s based before introducing any changes. It consisted of a two layer model in which the bottom layer was driven solely by the barotropic tides as given by Crean's (1978) numerical t i d a l model of the S t r a i t of Georgia. The area covered by the model was bounded by Vancouver Island, the mainland and two open boundaries, one along a transect about 8 km to the northwest of Nanaimo and another one about 10 km to the southeast of Boundary Pass. Boundary Pass i t s e l f was l e f t open. The timestep and the grid size were respectively 120 sec and 2 km in the f i n a l version of the model. The governing equations for the upper layer were expressed as follow: 9h/9t+9U/9x+9V/9y = w -w P n 4.1 9S/9t+9(US/h)/9x+9(VS/h)/9y = w s0-w S/h P n 4.2 9U/9t+9(U2/h)/9x+9(UV/h)/9y+9(g'h2/2)/9x-fV 1/2 +KU (U 2+V 2) R R R /h2+h9(A9(U/h)/9x)/9x +h9(A9(U/h)/9y)/9y = u0w -(U/h)w -gh9$/9x P n 4.3 70 3V/3t+3(u^/h)/3x+3(V2/h)/3y+3(g'h2/2)/3y+fU 1/2 +KV (U 2+V 2) R R R /h2+h3(A3(V/h)/3x)/3x +h3(A3(V/h)/3y)/3y = v0w -(V/h)w -gh3$/3y P n 4.4 where U,V are v e r t i c a l l y integrated transports for the upper layer (cm 2/s), g'=gAp//o, the s p e c i f i c gravity (cm/s 2), A= horizontal eddy v i s c o s i t y (cm 2/s), $= barotropic t i d a l elevation (cm), S= v e r t i c a l l y integrated s a l i n i t y (cm(o/oo)), Vo/ vo= t i d a l streams (cm/s), U , V = r e l a t i v e transports =U-u0h, V-v 0h (cm 2/s), R R K= quadratic f r i c t i o n c o e f f i c i e n t , w = entrainment ve l o c i t y (cm/s), s 0= constant s a l i n i t y of the water underneath the plume (o/oo), h= plume thickness (cm), f= C o r i o l i s parameter (sec ). This system of equations was solved for h,U,V and S. Reflecting the strong dependence of density on the s a l i n i t y of the plume water, an empirical equation of state was used: P w = depletion v e l o c i t y (cm/s), n -1 = 24.0-(0.8S/h). 4,5 The entrainment ve l o c i t y took the f i n a l form: 71 1/2 w = 0.0001(U2+V2) /h. 4.6 p R R This expression was similar to the one given by Keulegan (1966) for the arrested s a l t wedge entrainment: w = 0.000212 (u-u ) 4.7 P c where u for the Fraser r i v e r i s about 3 cm/s (Cordes et c a l . , 1980). This was a departure from a suggested expression for the entrainment v e l o c i t y that included a dependence on the lo c a l Richardson number ( E l l i s o n and Turner, 1959). The depletion v e l o c i t y (the v e r t i c a l v e l o c i t y associated with the water going from the plume to the bottom layer) was introduced to thin the plume in the outer regions (away from the Fraser River mouth). This v e l o c i t y was then made dependent on the s a l i n i t y through the expression: w = (1-exp(S/(I0h)))h/200 4.8 n This expression had no observational or theoretical support. It was the result of a suspected dependence of the depletion on the s t r a t i f i c a t i o n in the outer regions and of various modelling tests introducing t h i s term (Stronach, 1977). The terms with K in the momentum equations (4.3 and 4.4) are intended to model the i n t e r f a c i a l f r i c t i o n . K took values from 0.001 to 0.007. The wind stress was neglected in the model. The horizontal eddy c o e f f i c i e n t (A) used varied from 103 to 10" cm 2/sec. The flow at the open boundaries was governed by the 72 constraint: 9 2F 2/dn 2 = 0, 4.9 namely that the second derivative of the Froude number squared (F 2=U 3/g'h 3) normal to the boundary was to be zero. Various boundary conditions have been t r i e d (Stronach, 1977) but t h i s one has the advantage of allowing the flow to reverse at the boundaries. The s a l i n i t i e s at the open boundaries were extrapolated from the neighboring inside g r i d points. These boundary conditions were put forward on the argument of slowly varying conditions far from the Fraser River mouth. The s o l i d boundaries required no flow normal to them. The main concern of t h i s model was the effect of the t i d a l forcing and for this reason i t was never run for more than 24 to 48 hours. V e l o c i t i e s and s a l i n i t i e s were i n i t i a l l y set to zero everywhere while the i n i t i a l plume thickness was set to 150 cm. 5.2 General Modifications Of The Existing Model The main purpose of a modelling e f f o r t in the context of t h i s research i s to relate variations of the observed "ferry" s a l i n i t i e s to the effects of physical dynamical processes that can be quantified. As seen in the previous chapters, the ferry data most accurately define long-term variations while the t i d a l fluctuations are only marginally resolved. The computing e f f o r t should then emphasize the long-term variations due mainly to discharge and wind. This implies running the model for periods on the order of 10 to 20 days. In order to reduce computer cost, i t was decided to s a c r i f i c e s p a t i a l resolution to a 73 limited extent. The grid size was increased from 2km to 3 km. This gr i d size s t i l l respects the s t a b i l i t y c r i t e r i a given in the appendix of Stronach's work (1977) and allows a minimum of resolution for the plume property d i s t r i b u t i o n s . S i m i l a r l y , the area covered by the model was reduced to a minimum, namely enough to include the two ferry sections (Fig. 20). The effect of the positions of the open boundaries was investigated by running a preliminary windless model with one or two supplementary gri d rows beyond the southeast and northwest ends of the model. The present positions of the open boundaries (Fig. 20) seem to leave the s a l i n i t i e s near the ferry sections unaffected within the l i m i t of the measurement error. The f i r s t model-geometry to be used included Boundary Bay that was located in the lower right corner of F i g . 20. It was decided to delete i t from the modelling area because of computational i n s t a b i l i t y a r i s i n g from the open boundary conditions when a southerly wind was acting. Another solution to that problem could have been to move the southern open boundary even farther away from the river mouth but t h i s model would have been more costly to run. No water was allowed to go over the shallow sand f l a t s on the south eastern side of the rive r mouth. The orientation of the g r i d points r e l a t i v e to the map of the S t r a i t of Georgia was decided by aligning the southern ferry section with a row of g r i d points. The set of coordinates used for the numerical model i s indicated in F i g . 20. This set of coordinates was used by Stronach (1977). It should be noted that t h i s set d i f f e r s from the set of coordinates defined in the previous 74 NANAIMO ACTIVE PASS BOWEN ISLAND VANCOUVER Figure 20 - Grid used by the numerical model showing the two ferry tracks and the set of coordinates used chapters; i t i s rotated by 183° r e l a t i v e to the former. Stronach's set of coordinates was only used i n t e r n a l l y , within the framework of the model and I s h a l l hold for the rest of the 75 discussion to the e a r l i e r convention. Special care was given to the i n i t i a l f i e l d s of h,U,V and S. It was f e l t that they should be as close as possible to " r e a l i s t i c " f i e l d s to avoid transient states. These i n i t i a l f i e l d s should characterize the general horizontal d i s t r i b u t i o n s for the s t a r t i n g day. They were obtained by running the model with a constant r i v e r discharge of 4130 m3/sec from constant f i e l d s (U=V=0 cm/sec, S=15 o/oo-150 cm and h=150 cm everywhere) u n t i l a steady state was reached. No t i d a l forcing was present in t h i s spin-up model, meaning that the bottom layer was at rest and the t i d a l slopes were n u l l . Otherwise, Stronach's model was l e f t intact with A and K given values of 103 cm2/sec and 0.001 respectively. The d i s t r i b u t i o n s of s a l i n i t y and v e l o c i t y obtained from thi s spin-up model are shown in F i g . 21. They are to be used as i n i t i a l conditions for further models. The action of the C o r i o l i s force i s quite evident in pushing the plume towards the northern section. From these steady state f i e l d s , the model is then run with slowly varying discharge and wind. The discharge is interpolated l i n e a r l y at each time step (every 2 minutes) between the d a i l y values monitored at Mission City s t a r t i n g on a day when the discharge i s 4130 m 3/sec. The wind, that was set to zero during the spin-up, i s brought back into the momentum d i f f e r e n t i a l equations at the same time as the discharge i s allowed to vary slowly. The term responsible for the wind in the equations comes from the parametrization of the surface stress, a term previously neglected in Stronach's work (1977). 76 NRNAIMQ 20 CM/S w / n J J 1 I \ i /1 i j i i i \ \ i /i j / / / / ^ r r 2 Q \ i i j i j/yj J i \ .. i i y y>7 / / / / / / \ i 1 J r 1 .1 J^y* ^ s RCTIVE PRSS BOWEN ISLRND Figure 21 - D i s t r i b u t i o n s of v e l o c i t y and s a l i n i t y used as i n i t i a l conditions. The s a l i n i t y contour labels have unit of o/oo and the t a i l of the v e l o c i t y vector i s located on the corresponding gr i d point 77 A few steps before getting equations 4.1 to 4.4, a term l i k e : n (1/p) J O r /9z)dz 4.10 z = £ x was present on the right hand side of the x-momentum equation (Stronach, 1977) . The surface elevation i s denoted by 7j and $ describes the position of the interface. This stress term can then be written as d / p ) ( ( r ) - ( T ) ) 4.11 X Z = TJ X z=£ The term - ( l / p ) ( r ) was parametrized by the expression x z=£ 1/2 -KU (U 2+V 2) /h 2. The wind stress ((r ) /p), that was R R R x z = 7} neglected previously, w i l l be replaced by the similar driving expression: 1/2 (C p /p)u (u 2+v 2) 4.12 D a w w w where u ,v are the wind components in the coordinate system of the w w model, p /p i s the r a t i o of the a i r and water density (0.0013) and a C i s the drag c o e f f i c i e n t . D S i m i l a r i l y , a term l i k e : 1/2 (C p /p)v (u 2+v 2) 4.13 D a w w w i s added on the right side of the y-momentum equation. The drag 78 c o e f f i c i e n t has been evaluated on an open ocean stretch (Large and Pond,1981): C = 0.0012 i f 4<U10<11 m/sec D C =0.001(0.4+0.065 U10) i f 11<U10<25 m/sec 4.14 D where U10 is the wind speed 10 m above the sea surface. For lack of better wind measurements U10 w i l l be substituted for the wind speed measured at Entrance Island wind station. The choice of using Entrance Island wind data instead of Sand Heads wind record should not affect the results s i g n i f i c a n t l y since the two data records are highly correlated for the long-term variations. Hourly wind data for each component were interpolated l i n e a r l y at each time step. In the course of running the model, the open boundary condition for the s a l i n i t y along with the high v e l o c i t i e s at the boundaries due to the wind produced upper layer s a l i n i t i e s larger than the s a l i n i t y of the bottom layer. Specifying a n u l l f i r s t derivative of the s a l i n i t y normal to the open boundary got r i d of t h i s i n s t a b i l i t y . Comparison between the output of the model and the ferry observations requires some syntheses of the s a l i n i t y variations near the ferry sections. As before the average s a l i n i t y along a ferry section would seem to be the appropriate c h a r a c t e r i s t i c for each section. An equivalent average s a l i n i t y for the southern section is computed as the arithmetic average of the s a l i n i t y at g r i d points along that section. For the northern section, fourteen values of s a l i n i t y along the section are 79 interpolated from the surrounding gr i d points. These values are then ar i t h m e t i c a l l y averaged to give an equivalent average s a l i n i t y for the northern section. The p o s s i b i l i t y of comparing the horizontal s a l i n i t y gradient was b r i e f l y investigated but the poor resolution of the numerical model along each section greatly underestimates the value of the s a l i n i t y gradient. The observed magnitudes of the s a l i n i t y gradient are also more scattered than the s a l i n i t y measurements. 5.3 Numerical Results With Variable Discharge And Wind Forcing With a mind to computational cost, periods with s i g n i f i c a n t changes in s a l i n i t y on inte r v a l s of a few days should be of more interest than slowly varying s a l i n i t y . It was mentioned in chapter 3 that the increase in discharge in the spring leads to rapid s a l i n i t y decreases while the decrease from that peak i s somewhat slower and so are the variations in s a l i n i t y . For t h i s reason, the emphasis was put on modelling the rapid decrease of s a l i n i t y in the springs. The periods to be modelled correspond to two of the cases already discussed in section 3.4, e s s e n t i a l l y the periods from J u l i a n days 119 to 139 and from Ju l i a n days 496 to 526 for the spring of 1980 and 1981 respectively. The abnormal December Peak discharge also received modelling attention. A l l of these three cases started on a day when the value of the r i v e r discharge i s close to 4130 m3/s. The same i n i t i a l f i e l d described in the previous section, was used for the three simulations. As seen in section 3.4 the combined ef f e c t s of the wind and 80 the discharge can q u a l i t a t i v e l y explain the d a i l y variations of the average s a l i n i t i e s . Thus the f i r s t modelling e f f o r t was to input the discharge and the wind into the model leaving out the t i d a l forcing. Here i t was assumed that most of the t i d a l e f f e c t i s averaged out over the period of a day. In other words, the fluctuations of s a l i n i t y due to the tides o s c i l l a t e s about a mean set by the conditions of the discharge and the wind. A li m i t e d model which includes the tides w i l l be the subject of the next section. 5.3.1 Comparison Of The Average S a l i n i t i e s The average s a l i n i t i e s from the ferry data are compared (Figs. 22 and 23) to the equivalent average s a l i n i t i e s from a model that d i f f e r s from the spin-up model only in that i t includes variable wind and discharge. The f i r s t case (Spring 1980) became unstable at J u l i a n day 123 and i s not shown. It happened right after a period of high northerly wind (the strongest along-strait wind in the three periods studied, (Fig . 12)) that induced plume v e l o c i t i e s on the order of 1 m/s. High values of entrainment of s a l t from the bottom layer follow via the d i r e c t proportionality of w on the plume v e l o c i t i e s . P The model stopped running because the s a l i n i t y near the northern section got beyond the s a l i n i t y of the bottom layer, inducing rapidly growing i n s t a b i l i t i e s . Such a problem did not occur for the two other cases (Figs. 22 and 23). Nevertheless, the same process of overestimating the s a l i n i t y of the plume occurred. This is e s p e c i a l l l y true for s a l i n i t y along the northern 81 DECEMBER PERK o LU CO O LU o LD V -H+ + + I I 1 1 1 356 .0 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 3 7 2 . 0 376 0 T J M E ( J U L I A N D A Y S ) i — i LOUD 3 5 6 . 0 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 3 7 2 . 0 T I M E ( J U L I R N D A Y S ) 3 7 6 . 0 Figure 22 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time for the December Peak using a model similar to the one of Stronach but with variable wind and discharge and no t i d a l forcing 82 SPRING 1981 o O on CJ) LoJ CO o f - DZ LO I I 1 1 1 49€ .0 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 5 2 0 . 0 526 0 T I M E ( J U L I A N D A Y S ) 4 9 6 . 0 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 T I M E ( J U L I A N D A Y S ) 520 .0 5 2 6 . 0 Figure 23 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model similar to the one of Stronach but with variable wind and discharge and no t i d a l forcing 83 section. No wind or discharge effects are c l e a r l y v i s i b l e in the v a r i a t i o n of the model s a l i n i t y on that section. For the southern section, the situ a t i o n i s much better. Overestimation of the s a l i n i t y s t i l l occurred but to a lesser extent. The wind more than the discharge seems to dictate the variations of the s a l i n i t y on the southern section. . The r i s e of s a l i n i t y from Ju l i a n days 502 to 503, 506 to 512, 518 to 524, 358 to 364 and f i n a l l y from 372 to 376 are a l l associated with southeasterly winds (Figs. 13 and 14). Inversely the drops in s a l i n i t y occurred during northwesterly winds. Advection due to the wind can explain these effects on the model s a l i n i t y . Clearly the model, as i t i s , overestimates the flux of salt into the.plume. This s a l t can come from the bottom layer or be advected l a t e r a l l y through the open boundaries. The l a t t e r source of s a l t i s not thought to be the major one because of the special form of the open boundary condition for s a l t . The advected s a l t from outside of the modelling area was set to equal the s a l i n i t y just inside the open boundary. The major source of s a l t must then be the bottom layer. The s a l t i s brought in the plume via the entrainment v e l o c i t y that depends on the plume v e l o c i t i e s that are themselves greatly affected by the wind. Another conclusion resulting from the analysis of Figs. 22 and 23 i s that the effect on the model of the varying discharge i s minimal. The annual discharge pattern i s too obvious in the observed variations of the average s a l i n i t y (ref section 3.1) to be neglected, especially in the case of the December Peak for 84 which the abnormal drops in s a l i n i t y are without a doubt due to high discharge. The model inputs the variation of the discharge through variations of the v e l o c i t y and depth of the layer at the r i v e r mouth using the hypothesis that there the Froude number i s one. The effect of an increased discharge of fresh water i s partly erased by the increase in entrainment due to the v e l o c i t y increase at the mouth. The December Peak case was run without wind input and on both sections, a drop of only 1 to 2 o/oo resulted from the sharply varying discharge. The necessity of decreasing the entrainment v e l o c i t y and providing more response to the discharge suggested a change to an entrainment v e l o c i t y that depended on the s t r a t i f i c a t i o n . Numerous studies (Long 1975 and 1978) and experiments in water tanks (Wu, 1973; Kato and P h i l l i p s , 1969; Kantha, P h i l l i p s and Azad, 1979) and under natural conditions (Kullenberg, 1977) tend to show a dependency of the entrainment on an o v e r a l l Richardson number R defined as i * R = g'h/u 2 4.15 i * * where u i s the f r i c t i o n v e l o c i t y . Some of the above * papers suggest the expression: -1 tf = Cu R 4.16 p * i * but i t i s questionable in the l i g h t of the more recent results of Kantha et a l . (1977). The problem in using t h i s expression is the evaluation of the f r i c t i o n v e l o c i t y and i t s 85 rel a t i o n to the cause of the turbulence. McClimmans (1980) l i s t e d sources of turbulent entrainment in plume. Wu (1973) and Kullenberg (1977) relates u to the wind stress but, near the * river mouth, winds of the order of 100 km/hr would be needed to produce the measured entrainment (Cordes et a l . , 1980). If the entrainment i s shear generated, u could be proportional to the * v e l o c i t y difference between the two layers as was done in Long (1975) assuming a c r i t i c a l flux Richardson number. Under this assumption, the entrainment depends on g'h 3/U 3, that i s the inverse of the Froude Number squared, and the entrainment takes the form: n w =C,u(F2) 4.17 P where n has the value of 1. Several runs of the model for the December case were performed varying the posi t i v e exponent n. A l l of them f a i l e d to model the expected drop in s a l i n i t y . Stronach (1977) had also noticed the f a i l u r e of t h i s expression that made the entrainment a function of the plume v e l o c i t y to the power 3. A more dire c t dependence on the s t r a t i f i c a t i o n was then t r i e d using the expression: r w = 0.0001 (U/h) (s/s 0) 4.18 P where s i s the s a l i n i t y of the plume and r, an exponent to vary the dependence of w on the s t r a t i f i c a t i o n . With r = 0, P Stronach 1s expression for the entrainment velocity i s recovered. r The factor ( s / s 0 ) i s always smaller than one and entrainment 86 values near the mouth are lower than in the far f i e l d . The introduction of this reducing factor i s also consistent with the o v e r a l l trend that can be seen in the entrainment c o e f f i c i e n t of Cordes et a l . (1980) according to which high ratios w /u are P found at small s a l i n i t y differences between the upper and lower layers. This expression of entrainment with r=0.75 used in a model of the December case with variable discharge, but no wind, induced a drop of s a l i n i t y on the northern section of the right order of magnitude (10 o/oo). Subsequently, i t was found that the drop was mainly caused by the t r a n s i t i o n between the steady state obtained with Stronach 1s expression to the one with reduced entrainment due to s t r a t i f i c a t i o n . No increase in the discharge was needed to produce the drop in s a l i n i t y and the f a l l in s a l i n i t y started on the f i r s t , day (356) instead of on day 361 as shown by the ferry data. A change in the expression of the entrainment was needed to produce the expected drop which should be related to changes in the conditions of the forcing on the plume. It i s suggested that the discharge could be the related forcing parameter that changes the o v e r a l l effect of the s t r a t i f i c a t i o n on the mixing and entrainment of salty water in the plume by default of a more l o c a l parameter. It should be remembered that the s a l i n i t y factor in eq. 4.18 mostly a f f e c t s the area near the river mouth. At a medium discharge, l i k e the one used to get the steady state, we want the entrainment to depend weakly on the s t r a t i f i c a t i o n and change to depend strongly on the s t r a t i f i c a t i o n at high discharge. This i s done by making the 87 exponent r in the expression of the entrainment (eq. 4.18) a function of the discharge. To avoid a sudden t r a n s i t i o n from the steady state f i e l d s obtained with Stronach's entrainment r w i l l be set to zero for a discharge of 4130 m3/s. The simplest function to use i s a l i n e : r = (D-4130)/C2 4.19 where D i s the discharge in m3/s. The constant C 2 has been determined by running the spring 1981 model and trying to obtain the general trend of the northern section s a l i n i t y decrease. A cut-off discharge was necessary to stop the s a l i n i t y from decreasing even further. F i n a l l y , the expression for the entrainment exponent, r = 0 i f D < 4130 m3/s, r = (D-4130)/2000 i f 4130 < D < 5130 m3/s, r = 0.5 i f D > 5130 m3/s, 4.20 was used in the run for which the average s a l i n i t i e s are compared with the Ferry data for the Spring 1981 in F i g . 24. The reduced entrainment mainly a f f e c t s the general decrease of the s a l i n i t y on the northern section. For the southern section, a more important drop in s a l i n i t y between Julian days 513 and 519 i s noticed i f compared to the results in F i g . 23. In spite of these improvements, the general overestimation of the s a l i n i t i e s s t i l l remains. If t h i s expression for the entrainment v e l o c i t y i s applied to the December Peak case with wind input, no s i g n i f i c a n t changes are observed from the results in F i g . 22. The spring 1980 case s t i l l stopped running after 5 days, just after the period of high winds. The reduced 88 SPRING 1981 4 9 6 . 0 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 5 2 0 . 0 5 2 6 . 0 > - T I M E ( J U L I A N D A Y S ) l— co CD i i i i r 4 9 6 . 0 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 5 2 0 . 0 5 2 6 . 0 T I M E ( J U L I A N D A Y S ) Figure 24 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time for the Spring 1981 using a model similar to the one leading to F i g . 23 but with reduced entrainment v e l o c i t y 89 entrainment did not help in eliminating the i n s t a b i l i t i e s . This result should have been expected since they occur due to large entrainment in regions of high s a l i n i t y for which the new expression of entrainment does not change anything. The solution was found in the modification of the effect of the source of salty water entrainment i.e. the wind. A f i r s t improvement was achieved by reducing the wind input for regions of high s a l i n i t y . The reason behind this change, i s that for plume water with s a l i n i t y close to 29 o/oo, the plume water cannot be d i f f e r e n t i a t e d from the bottom layer water. It was assumed so far that the wind momentum transfer i s uniformly d i s t r i b u t e d in the upper layer, but in a poorly s t r a t i f i e d s i t u a t i o n one can imagine that the wind action could extend beyond the plume thickness so that the plume i t s e l f only gets a fraction of the momentum input from the wind. This modification is achieved by a r b i t r a r i l y multiplying the drag c o e f f i c i e n t by a factor (F,) which depends on the s a l i n i t y and goes to 0 when no s t r a t i f i c a t i o n i s present. A smoothed t r a n s i t i o n is included from a s a l i n i t y of 25 o/oo and over. The general expression used for t h i s factor i s F, = b i f s < 25 o/oo F, = b-b(s-25)/4 i f 25 < s < 29 o/oo. 4.21 T h e ' i n s t a b i l i t i e s for spring 1980 vanish with the introduction of t h i s factor with b=1. The results for thi s case with Stronach's entrainment expression and with the reduced entrainment of equation 4.18 are displayed in Figs. 25 and 26, respectively. The two sets of curves are not q u a l i t a t i v e l y much 90 SPRING 1980 O c t : , 2 1 CD 4 V I 1 1 1 119.0 123.0 127.0 131.0 135.0 TJM£ ( J U L I A N D A Y S ) 1 1 9 . 0 T 123.0 127.0 131.0 135.0 T I M E ( J U L I A N D A Y S ) 1 139.0 139.0 F i g u r e 25 - P l o t s of the average s a l i n i t y f e r r y data (crosses) and modelled average s a l i n i t y ( s o l i d l i n e ) vs time f o r the S p r i n g 1980 using a model with the entrainment v e l o c i t y of Stronach and a reduced wind f a c t o r (b=1.) 91 SPRING 1980 119 .0 123 .0 127 .0 1 3 J . 0 135 0 T I M E ( J U L I A N D A Y S ) 1 3 9 . 0 119 .0 123 .0 127 .0 131 0 135 0 T I M E ( J U L I A N D A Y S ) 139 .0 Figure 26 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time for the Spring 1980 using a model with a reduced entrainment vel o c i t y and a reduced wind factor (b=l) 92 L J LU CO O LU O 01 o O L J LU C E co o CO co _J ct: LU ZD O SPRING 1981 i 1 1 1 — 4 9 6 . 0 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 5 2 0 . 0 T I M E ( J U L I A N D A Y S ) 5 2 6 . 0 4 9 6 . 0 , , , 5 0 2 . 0 5 0 8 . 0 5 1 4 . 0 5 2 0 . 0 T I M E ( J U L I A N D A Y S ) 5 2 6 . 0 Figure 27 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1981 using a model with reduced entrainment v e l o c i t y and with a reduced wind factor (b=0.5) 93 d i f f e r e n t from each other. The f i r s t expression of entrainment leads to a better comparison on the southern section than with reduced entrainment while the decreasing trend of s a l i n i t y on the northern section seems best reproduced when the reduced entrainment i s used. Both model runs f a i l to explain the secondary fluctuations ( l i k e the peak between Jul i a n days 133 and 135) that are superposed on the general trend of the northern section s a l i n i t y . This was also noticed for the Spring 1981 case (Fig. 24). The peak in s a l i n i t y on the northern section between day 510 and 513 never appears to be modelled. These fluctuations might not be wind related. On the other hand, the model s a l i n i t y on the southern section responds strongly to the wind input. The southeasterly wind during periods 125-129 and 131-134 are associated with the r i s e of the s a l i n i t y and the drops in s a l i n i t y correspond to the onset of northwesterly winds. If the Spring 1981 case i s run using the reducing factor F, with b=0.5 (Fig. 27), the overestimation of s a l i n i t y on the southern section i s reduced, especially between Jul i a n days 508 and 513. The s a l i n i t y trend on the northern section agrees better than in F i g . 24. A "b" equal to 0.125 for the wind factor in the December Peak i s necessary to achieve the agreement in F i g . 28. Again the overestimation of the southern section s a l i n i t y between Julian days 361 and 366 i s d e f i n i t e l y eliminated by reducing the wind e f f e c t . The s a l i n i t y drop on the northern section i s modelled to some extent. An even lower entrainment v e l o c i t y 94 DECEMBER PERK o (_> LU V ) q £ o CD ^ A * + 3 5 6 . 0 T 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 372 0 TIME (JULIAN DAYS) i — i CO to 3 5 6 . 0 1 r — 1 r 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 372 0 TIME (JULIAN DAYS) 3 7 6 . 0 1 3 7 6 . 0 Figure 28 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l i n e ) vs time for the December Peak using a model with reduced entrainment and with a reduced wind factor (b=0.125) 95 (for example with an exponent r=0.75 ) would be needed to simulate a drop of 10 o/oo, but the slow increase of the model s a l i n i t y would s t i l l be present. The fact that the December Peak case needs a lower wind factor than the two Spring cases can be explained by remembering that during the winter wind storms destroy the s t r a t i f i c a t i o n and more well mixed water i s present than during the spring. In trying to find the best exponent r to use in the entrainment expression, the northern section s a l i n i t i e s were r e l i e d on because the southern section s a l i n i t i e s were not as sensitive to changes in the entrainment v e l o c i t y due to discharge fluctuations. On the other hand, the values of the c o e f f i c i e n t b in the wind factor F, were found using the southern section s a l i n i t i e s because the northern section s a l i n i t i e s did not respond as strongly to changes in the wind factor. This seems to be in agreement with an observation made in section 4.1 according to which higher correlations between the s a l i n i t y and the discharge were found on the northern section r e l a t i v e to the southern section while smaller correlations between the wind and the average s a l i n i t y were computed on the northern section as compared to the southern section. 9 6 5.3.2 Quantitative Estimate Of The Agreement Between The Model  And The Ferry Observations The q u a l i t a t i v e agreement between the model and the ferry measurements w i l l be quantified in t h i s subsection using cross-correlations between the d a i l y average s a l i n i t i e s (model and ferry data) and the root mean square (RMS) error between the two seri e s . The model d a i l y average s a l i n i t y i s obtained from hourly values averaged with the same f i l t e r as a l l other d a i l y average estimates, namely a 48-hr B a r t l e t t f i l t e r . Table X summarizes the cross-correlation results for the d i f f e r e n t model runs. These are separated into three types: those with the unchanged wind and entrainment expressions, those with reduced entrainment and t h i r d l y the ones with reduced wind and entrainment factors. The c l a s s i f i c a t i o n for the Spring 1980 case d i f f e r s s l i g h t l y in that a l l successful runs required a reduced wind input at high s a l i n i t y . The two runs are then c l a s s i f i e d under the entrainment expression used. No further reduction of the wind was judged necessary for the Spring 1980 case, so that no results appear for the change of wind factor. The f i r s t conclusion to be drawn from Table X i s that the southern section i s better described by the model than the northern section. This could simply be due to the fact that the southern section i s closer to the Fraser River mouth and so under a more di r e c t influence of the plume than the northern section for which other mechanisms or fresh water inputs could become important. A change in the entrainment expression does not seem to influence the correlation for the southern section 97 Table X - Cross-correlations and time lags between the average s a l i n i t i e s of the model and of the ferry data Model with Stronach's entrainment and wind factor equal to 1 Model with reduced entrainment and wind factor equal to 1 Model with reduced entrainment and reduced wind factor Spring 1980 Southern section Northern section 0.84 at day lag 0 no s i g . correlat ion 0.84 at day lag 0 no s i g . correlation the same as the model with a wind factor equal to 1 December Peak Southern section Northern section 0.68 at day lag 2 no s i g . correlat ion 0.69 at day lag 2 no s i g . correlation 0.83 at day lag 0 0.83 at day lag 2 Spring 1981 Southern section Northern section 0.85 at day lag 0 no s i g . cor r e l a t i o n 0.85 at day lag 0 0.67 at day lag 2 0.89 at day lag 0 0.71 at day lag 1 s a l i n i t i e s while a change in the wind expression has the potential of s l i g h t l y increasing the correlation c o e f f i c i e n t and improving the time lag which should be equal to 0 in the case of perfect agreement. The poor correlation encountered in the case of the northern section s a l i n i t y can be attributed to the preliminary detrending of the time series previous to the cross-c o r r e l a t i o n computations. Previous q u a l i t a t i v e agreement (ref section 4.3.1) between the average s a l i n i t i e s (model and ferry data) could have come uniquely from the general trend, that same 98 Table XI - Root mean squared error (o/oo) between the model and the ferry data average s a l i n i t i e s Model with Stronach's entrainment and wind factor equal to 1 Model with reduced entrainment and wind factor equal to 1 Model with reduced entrainment and reduced wind factor Spring 1980 Southern sect ion Northern section 1 .30 1 .97 2.68 1 .68 the same as the model with a wind factor equal to 1 December Peak Southern section 5.61 5.49 3.06 Northern sect ion 5.65 5.43 2.4-1 Spring 1981 Southern sect ion 4.43 3.37 2.15 Northern sect ion 4.12 2.22 1 .73 trend that i s lost during the detrending procedure. In other words, the good agreement in the northern section s a l i n i t y trends can not be revealed by the cross-correlation c o e f f i c i e n t s . The eff e c t of the reduced entrainment i s seen to produce a s i g n i f i c a n t c o r r e l a t i o n for the Spring 1981 northern section s a l i n i t y . Even further improvement in the cor r e l a t i o n and phase is achieved by reducing the wind by a factor of two for that spring case. For the December Peak, the introduction of a reduced wind d e f i n i t e l y improves the correlations for both 99 sections. The ef f e c t of the reduced entrainment was masked by high wind e f f e c t s . When these are reduced, changes in the entrainment expression can be shown to mostly a f f e c t the northern section s a l i n i t y . Cross-correlations only investigate the possible r e l a t i o n between the fluctuations of the two time series and disregard the amplitude of the fluctuations and the absolute values of the elements in the series. Table XI looks at the root mean square error between the model and the observed data. Successive improvements in decreasing the RMS error are achieved by introducing a reduced entrainment followed by a reduced wind input. It i s only in the case of the southern section s a l i n i t y for the Spring 1980 case that a worsening of the error is noticed. The cross-correlation has been seen to not have been affected by t h i s change. On the other hand, the ef f e c t of the reduced entrainment can be seen in Table XI to improve the agreement between the model and the ferry data on the northern section for that case. The low values for the RMS error on that section r e f l e c t s the good q u a l i t a t i v e agreement of Figs. 25 and 26 that was hidden in the evaluation of the cross-correlations because of the detrending. In b r i e f , for the spring 1980, good agreement between the observations and the model depends weakly on the entrainment velocity expression used. This i s not the case for Spring 1981 for which the s a l i n i t y error on the northern section i s reduced by a factor of 1.9 by the use of the reduced entrainment compared to a reduction by a factor of 1.3 with the introduction of a reduced wind factor. On the other 100 hand, the wind factor reduces the error to a larger extent than the entrainment velocity expression for the Spring 1981 southern section comparison. For the December Peak, one should not conclude from the small improvement in the error s i z e , coming from the change in the entrainment expression, to a deficiency of t h i s parameter to improve the c o r r e l a t i o n . An overwhelming wind input in this case is more l i k e l y to hide any improvements brought by the modification of the entrainment v e l o c i t y . 5.4 Numerical Results Including T i d a l Forcing Remembering the poor resolution of the ferry data for fluctuations at t i d a l frequencies, i t seems unwise to proceed with an extensive and precise modelling e f f o r t to include the tides for the sake of the comparison with the ferry data. The emphasis was instead to include t i d a l e f f e c ts in the model only as approximations of the t i d a l currents and the modulation of the discharge by the tides. The aim i s also to check i f the inclusion of the t i d a l forcing confirm the conclusions found so far for the e f f e c t s of the discharge and the wind. T i d a l forcing in Stronach's model was input through the barotropic slopes (the terms gh9$/9x and gh9$/9y in equations 4.3 and 4.4), through the barotropic currents in the bottom layer (u 0,v 0) and the modulation of the discharge, at t i d a l frequencies. The t i d a l slopes and currents were input from Crean's barotropic model every 15 minutes (Stronach,1981), but u n t i l the l a t t e r model was available, approximate amplitudes for the t i d a l slopes and currents were used (Stronach,1977). The 101 present study has made use of these approximations. Only fluctuations at the diurnal (K,) and the semi-diurnal (M2) periods were considered. The phases were referenced to the phases <t>^ and <p2 of the K, and M2 constituents for the sea le v e l elevation at Point Atkinson. Phases <6, and <t>2 were computed from harmonic analysis of the sea l e v e l elevation for which the time o r i g i n of the analyses coincides with the s t a r t i n g days of the three modelling cases. An average value of 23 cm/s for the M2 current amplitude can be inferred from F i g . 114 of Stronach's thesis (1977). Parker (1977) reports current measurements in the S t r a i t indicating a r a t i o of 0.6 between the t i d a l amplitudes of the K, and M2 currents. The phases of the two constituents of the barotropic t i d a l v e l o c i t y were computed from near surface current measurements on sections close to the ferry sections (Data Record of Current Observations,1969-1970). The f i n a l expression for the t i d a l current i s u 0 = 0 cm/sec, v 0 = -(13.8 cos(u,t - (0,-84 o ) /36O°) + 23 cos(w 2t - ( 0 2-75°)/36O°) cm/s, 4.22 where and co2 are the angular frequencies of the K, and M2 constituents respectively. It i s assumed that the a c r o s s - s t r a i t t i d a l current i s n u l l . As a poor approximation, geostrophy i s assumed to hold for the along-strait current component so that the a c r o s s - s t r a i t slope i s estimated as follows: 3$/3x = f v 0 / g . 4.23 The along-strait slopes, on the other hand, are approximated 102 from the same figure of Stronach's thesis as used for the t i d a l currents. The amplitude of the M2 slope has been estimated to be 5.24 cm/2 km. This slope has an out-of-phase relationship with the sea l e v e l elevation and the r a t i o of the amplitudes of the K, and M2 slopes i s the same as the r a t i o of the amplitudes of the sea l e v e l elevation, that i s 0.94. F i n a l l y the along-s t r a i t slope i s written as -6 3S/9y = -(2.46-10 cos(co 1t -c6 1 ) -6 + 2.62-10 cos(o) 2t-0 2) ) cm/cm. 4.24 Uniformity of the currents and slopes over the modelling area are a further approximation for the sake of s i m p l i c i t y and a reduction of the number of parameters. The modulation of the discharge by the tides i s modelled by adding to the ve l o c i t y at the r i v e r mouth diurnal and semi-diurnal fluctuations. The amplitude and phases of these fluctuations are obtained from the harmonic analysis of a current meter record located at the r i v e r mouth (Stronach,1977). The t i d a l l y modulated speed at the river mouth (u ) i s taken as: m u = u +33 cos(w 1t-(0 l+138°)/36O°) m c + 48 c o s ( c j 2 t - U 2 + l52°)/360°)) cm/sec 4.25 where u i s the speed at the mouth computed from the d a i l y c discharge value. Tidal forcing was added to the computer model and run for the three cases previously described. For each case, the wind 103 factor and the entrainment that gave the lowest RMS difference with the ferry data were used. No s i g n i f i c a n t changes in the model average s a l i n i t i e s were noticed i f only the t i d a l modulation of the discharge was added. On the other hand, the entrainment v e l o c i t y had to be multiplied by a factor of 0.75 in order to preserve the same general trend of the average s a l i n i t y as before when the underlying current and the t i d a l slopes are present. No reduction of entrainment would have been necessary i f the amplitude of the t i d a l current had been smaller than the residual v e l o c i t y due to the wind and the discharge. Figs. 29, 30 and 31 show the t i d a l l y forced model average s a l i n i t y in comparison to the ferry data. Perfect agreement i s not reached; nevertheless, the combined effect of the discharge and the wind i s s t i l l c l e a r l y v i s i b l e and set, as was assumed, the average conditions of the d i s t r i b u t i o n s of s a l i n i t y on which t i d a l fluctuations are superposed. This fact j u s t i f i e s the preceding analysis that neglected the t i d a l forcing as a f i r s t approach. Large t i d a l fluctuations of the model s a l i n i t y are found to coincide with periods of high scattering of ferry data and high ri v e r discharges. This observation corresponds to the previous conclusion from F i g . 19 that the eff e c t s of high t i d a l amplitudes on s a l i n i t y are found during periods of high rive r discharges. Harmonic analysis was performed with the model s a l i n i t y and the ferry data for the three cases studied and the results are compiled in table XII. Amplitudes and Phases of the model s a l i n i t y fluctuations do not vary over a wide range of values 104 SPRING 1980 o (_J LU CO CD 1 — ; CrT O LU 2 ^ CD * 4 4 * ^ I I 1 - — I — 1 2 3 . 0 1 2 7 . 0 131 .0 135 0 T J ME ( J U L I A N D A Y S ) 139 .0 I—I o 119 .0 1 2 3 . 0 1 2 7 . 0 1 3 1 . 0 1 3 5 . 0 T I M E ( J U L I A N D A Y S ) 1 3 9 . 0 Figure 29 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the Spring 1980 using a model with a reduced entrainment v e l o c i t y , a reduced wind factor (b=l) and with t i d a l forcing 105 DECEMBER PERK L J LU CO - J HZ 3 5 6 . 0 n i 1 1 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 3 7 2 . 0 T I M E ( J U L I A N D A Y S ) 3 7 6 . 0 i — i O o o <_J C O co LU LOCO + ± * V 4 ,++# + ' I 1 1 - T 1 3 5 6 . 0 3 6 0 . 0 3 6 4 . 0 3 6 8 . 0 3 7 2 . 0 376 0 T I M E ( J U L I A N D A Y S ) Figure 30 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d line) vs time for the December Peak using a model with a reduced entrainment, a reduced wind factor (b=0.125) and with t i d a l forcing 106 SPRING 1981 o CJ> U J ' - CO k — ' c e : O L U L> I— o LO 496 .0 1 I 1 1 502 0 508.0 514 0 520 0 T I M E ( J U L I A N D A Y S ) 5 2 6 . 0 o C E CO 1 ! ECT ++ 4 + LO ° .CO _ + c e : L U 4 J C 1 • 1 I D CQLD 4 9 6 . 0 5 0 2 . 0 5 0 8 . 0 514 0 520 0 T I M E ( J U L I A N D A Y S ) 5 2 6 . 0 Figure 31 - Plots of the average s a l i n i t y ferry data (crosses) and modelled average s a l i n i t y ( s o l i d l ine) vs time for the Spring 1981 using a model with a reduced entrainment v e l o c i t y , a reduced wind factor (b=0.5) and with t i d a l forcing 107 for the three cases for each section. The maximum difference of model s a l i n i t y amplitude i s 0.5 o/oo (seen between the Spring 1980 and December Peak southern section model K, s a l i n i t y amplitude) and the maximum change in phase Amplitudes and Phases of the model s a l i n i t y fluctuations do not vary over a wide range of values for the three cases for each section. The maximum difference of model s a l i n i t y amplitude is 0.5 o/oo (seen between the Spring 1980 and December Peak southern section model K, s a l i n i t y amplitude) and the maximum change in phase i s 60°. The Table XII - Amplitudes and phases from the harmonic analysis of the average s a l i n i t y of the model and the ferry data M2 Amplitude (o/oo) Phase (degree) Amplitude (o/oo) Phase (degree) Ferry Model Ferry Model Ferry Model Ferry Model Spring 1980 S. Section 0.7 1 . 1 190. 10. 1 .2 0.4 -10. 20. N. Section 0.3 0.3 20. 1 40. 0.3 0.3 1 30. 210. December Peak S. Section 0.9 0.6 -20. -30. 0.7 0.5 -70. 20. N. Section 0.2 0.4 180. 1 40. 0.2 0.2 120. 190. Spring 1981 S. Section 1 .6 0.8 -20. 30. 1 .4 0.6 -20. -0. N. Section 0.4 0.4 60. 1 40. 0.2 0.2 170. 170. phase values agree r e l a t i v e l y well with the phases expected from the. advection of the plume by the t i d a l current, that is an i n -phase relationship between the s a l i n i t y on the southern section 108 and the sea l e v e l elevation and an out of phase relationship between the northern section s a l i n i t y and the sea l e v e l elevation. The amplitudes indicate that, for both sections, the diurnal contribution to the s a l i n i t y fluctuations i s greater than the semi-diurnal one, even though the M2 constituent i s more important than the K, constituent for the t i d a l current and the sea l e v e l elevation. The dominance of the R, constituent over the M2 was also noticed in the yearly harmonic analysis of the Ferry data (Table IX). When the harmonic analysis results for the ferry data for the three cases are compared to the model harmonic r e s u l t s , the agreement i s far from perfect. Nevertheless, the difference between the phases are usually between -90° and 90° especially for the December Peak and the Spring 1981 cases. Surprisingly, the R, s a l i n i t y fluctuations for the Spring 1980 case of the Ferry data are almost out of phase with the same fluctuations for the model data. On the other hand, i f the model harmonic phase results are compared to the ferry data phases, obtained for the two years (Table IX), i t i s seen that these phases agree reasonably well with the model phases; however the fluctuations at the northern section do not show the out-of-phase relationship with the sea l e v e l elevation that the model predicted. Investigating the resemblance between the amplitudes of the model and the ferry fluctuations, one can estimate that the r a t i o of the two amplitudes varies from 0.4 to 3 over a wide range. In general, the amplitudes of the southern section ferry s a l i n i t y are greater than the corresponding model amplitudes 109 while the r a t i o of amplitudes on the northern section are usually less than or close to 1. One can presume that with a less uniform t i d a l current d i s t r i b u t i o n , for example a d i s t r i b u t i o n that would have high currents near the southern section and weak t i d a l currents near the northern section (as on F i g . 114 of Stronach's thesis, (1977)) that the amplitudes of the model fluctuations on the southern section would increase while the ones on the northern section would decrease and in th i s way more closely match the t i d a l amplitudes observed from the ferry data. 5.5 Horizontal Distributions Of The Plume Properties One purpose of the .model i s to provide horizontal d i s t r i b u t i o n s of the plume properties (U,V,h and s) in the area between the ferry tracks as a function of time. Because of the l o c a l i z e d nature of the ferry data, no such d i s t r i b u t i o n can be usef u l l y compared to the ferry observations. The only possible comparison between model. horizontal d i s t r i b u t i o n s and observations i s with the horizontal mapping of CTD surface measurements. Only two cruises were completed during the model periods, the f i r s t one during the night of May 7 to 8, 1980 (on Julian days 127 and 128) and the second during May 11 to 12, 1981 (Julian days 496 and 497). To account for the non-synoptic character of the CTD measurements, the t i d a l numerical model of the Spring cases was run to produce d i s t r i b u t i o n s of the plume properties at each time a CTD station was deployed. From each d i s t r i b u t i o n the s a l i n i t y of the plume i s interpolated at the Figure 32 - Surface s a l i n i t y contour (o/oo) from the CTD cruise on May 7-8, 1980 (Julian days 127-128). The crosses indicate the positions of the CTD stations 1 1 1 Figure 33 - Surface s a l i n i t y contour (o/oo) as given by the numerical simulation of the cruise of May 7-8, 1980 (Julian days 127-128). The crosses indicate the positions of the CTD stations 1 12 Figure 34 - Surface s a l i n i t y contour (o/oo) from the CTD cruise on May 11-12, 1981 (Julian days 496-497). The crosses indicate the positions of the CTD stations 1 13 Figure 35 - Surface s a l i n i t y contour (o/oo) as given by the numerical simulation of the cruise of May 11-12, 1981 (Julian days 496-497). The crosses indicate the positions of the CTD stations 1 14 position of the time corresponding to the CTD station. Contour maps of the set of these model s a l i n i t i e s for di f f e r e n t times and stations are shown in Figs. 33 and 35. They are compared to the corresponding contour maps from the CTD data (Figs. 32 and 34). The depth of the plume from the CTD data i s assigned to be the depth at which the maximum v e r t i c a l s a l i n i t y gradient occurs. The analogous CTD s a l i n i t y to the model i s computed by averaging the s a l i n i t i e s between the surface and thi s depth. The horizontal s a l i n i t y maps of Figs. 32 and 33 are the CTD and model d i s t r i b u t i o n s for the cruise during the Spring 1980. In general, the model produces lower s a l i n i t i e s at the mouth than the CTD data. This suggests that a possible modification of the model would be to have the ri v e r discharge s a l t i e r than 0 o/oo. The patch of fresh water with s a l i n i t y as low as 10 o/oo, near the northern section i s not modeled. These low s a l i n i t i e s are only recorded at one station so that i t could come from an error in the measurement operation at that station or an erroneous estimation of the plume thickness. Without i t , the horizontal s a l i n i t y gradient near the northern section would be lower and compare favorably with the model s a l i n i t y gradient. Near the southern section, the s a l i n i t y gradients are quite similar and the positions of the 22 o/oo isohaline near t h i s section are r e l a t i v e l y the same. .The same conclusion about the model underestimation of the s a l i n i t y at the mouth holds for the maps of the Spring 1981 case (Figs. 34 and 35). Contrary to the Spring 1980 where a quasi-symmetry seems to take place around the mouth, both model and 1 15 JULIRN DRY: 123 Figure 36 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 123 (May 3, 1980) 1 16 J U L I A N DAT : 130 * \\\ \ W X \ NANAIMO 20 CM/S BQWEN ISLAND A C T I V E P A S S X X K J. Jc > K Ji \ \ \ s, r \ \ \ \ X VANCOUVER Figure 37 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 130 (May 10, 1980) 1 17 JULIAN DAT: 132 NANAIMO 20 CM/S ACTIVE PASS BOWEN ISLAND Figure 38 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Jul i a n day 132 (May 12, 1980) 118 CTD d i s t r i b u t i o n s of s a l i n i t y show a freshening of the water towards the southern section. Considering a l l the l i m i t a t i o n s of the model (resolution, small area modelled, e t c . ) , the agreement between the CTD observations and the simulations is reasonably good. To show the time dependence of the s a l i n i t y on the discharge and the wind, horizontal d i s t r i b u t i o n s of s a l i n i t y and currents from the t i d e l e s s model for the three cases are plotted in Figs. 36 to 44. Each graph corresponds to a time at which an extremum of one of the average s a l i n i t i e s occurs. On day 123 (Fig. 36), strong northwesterly winds, of the order of 30 km/h, push the plume towards the southern section and are responsible for low s a l i n i t y on the southern section and high s a l i n i t y on the other section (Fig. 26). Model currents are well aligned with the d i r e c t i o n of the wind. On the contrary, the currents on day 130 (Fig. 37) are not in the same di r e c t i o n as the weak wind present at that time. The current pattern as for the s a l i n i t y d i s t r i b u t i o n i s reminescent of the southeasterly, four day long wind that ended 12 hours before. Strong p o s i t i v e (southeast) winds are r i s i n g again on day 132 (Fig. 38) greatly influencing the d i r e c t i o n of the surface currents. The s a l i n i t y d i s t r i b u t i o n does not respond as fast and is s t i l l vaguely characterized by the negative wind advection during J u l i a n day 130. For the December peak case, F i g . 39 shows the plume properties during high discharge and southeasterly wind (Julian day 361). The plume has d i f f i c u l t y reaching the southern 119 JUL J AN DAT: 361 NANAIMO 20 CM/S ACTIVE PASS BOWEN ISLAND Figure 39 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 361 (December 27, 1980) 120 JULIAN DAT: 365 F i g u r e 40 - S a l i n i t y (o/oo) and c u r r e n t d i s t r i b u t i o n s as given by a numerical model with v a r i a b l e wind and d i s c h a r g e on J u l i a n day 365 (December 31, 1980) 121 JUL]AN DAT : 376 NANAIMO 20 CM/S ACTIVE PASS BOWEN ISLAND Figure 41 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 376 (January 11, 1981) 122 section. It i s only when the wind has changed dir e c t i o n (Fig. 40) on Julian day 365 that the plume spreads over a l l the computational area. In thi s case, even with strong northwesterly winds, the currents are s t i l l outward from the riv e r mouth near the northern section. High discharge i s responsible for this spreading. F i g . 41 shows the plume properties d i s t r i b u t i o n s on day 376 when the discharge i s low again. This d i s t r i b u t i o n when compared to the d i s t r i b u t i o n of Fi g . 21, i s seen to resemble the steady state d i s t r i b u t i o n . The f i r s t chosen s a l i n i t y map for the Spring 1981 case describes a situation during a period of average southerly winds (Fig. 42 for Julian day 508). The wind pattern in the current is not as apparent as i t was during the Spring 1980 case for which the wind factor (F,) was set equal to 1. Nevertheless, the s a l i n i t y d i s t r i b u t i o n shows signs of a northward advection, consistent with the di r e c t i o n of the wind. The situation depicted in F i g . 43 (for Julian day 517) very much resembles the d i s t r i b u t i o n of F i g . 40. Both d i s t r i b u t i o n s occur at a time of high discharge and negative wind. The spreading of the plume in the Spring 1981 case is more intense r e f l e c t i n g the higher level of the discharge. F i n a l l y on Julian day 523 (Fig. 44) the r i s e of high southerly wind pushes the plume north, breaking the symmetry present on day 517. A few general observations that were discussed during the the examination of the ferry data in Chapter 3 are worth mentioning. It was noticed in that chapter that the s a l i n i t y on the southern section usually had a minimum at some point in the 123 JUL] AN DRY : 508 Figure 42 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 508 (May 23, 1981) 124 Figure 43 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Ju l i a n day 517 (June 1, 1981) 125 JULIAN DAT: 523 Figure 44 - S a l i n i t y (o/oo) and current d i s t r i b u t i o n s as given by a numerical model with variable wind and discharge on Julian day 523 (June 7, 1981) 1 26 middle of the section and not at x=1, as one might have assumed from the proximity of t h i s point to the river mouth. Most of the d i s t r i b u t i o n s of f i g s . 36 to 44 also indicate a high s a l i n i t y at x=1 on the southern section compared to a point in the middle of the section. In contrast, the d i s t r i b u t i o n s show a monotonic decrease of s a l i n i t y along the northern section except possibly on day 365 (Fig. 40) for which i t was already mentioned that during the December peak discharge, the lowest s a l i n i t y and the highest d a i l y variance were not found at x=1. 127 VI . CONCLUSIONS Comparisons between time series of average s a l i n i t y , maximum s a l i n i t y gradient and river discharge demonstrate that, for both northern and southern ferry sections, low s a l i n i t i e s and high horizontal s a l i n i t y gradients correspond to peaks in the rive r discharge. Cross-correlations and cross-spectra (coherence and phase) comfirm t h i s relationship especially at lower frequencies. In general the s a l i n i t y increases along each section towards Vancouver Island. In terms of da i l y variance in the north the plume appears to progress towards Vancouver Island during the June increase in discharge. No such progression i s seen along the southern section. In terms of frequency, possible wind and discharge contributions to plume v a r i a b i l i t y are well separated. Cross-correlations and cross-spectra between the plume c h a r a c t e r i s t i c s and the along-strait wind are compatible with the along-strait advection of the plume. A positive wind (blowing from the southeast) w i l l drive the plume to the northwest, r a i s i n g the average s a l i n i t y and lowering the s a l i n i t y gradient at the southern section; at the same time this advection w i l l sharpen the s a l i n i t y gradient and lower the s a l i n i t y at the northern section. A linear combination of the effects of wind and discharge was found to substantially improve the correlations between the plume c h a r a c t e r i s t i c s and the driving forces. Better q u a l i t a t i v e agreement was achieved using a non-linear combination where the wind contribution depends on the discharge 128 l e v e l . Harmonic analysis confirmed the combined ef f e c t s of t i d a l advection and t i d a l modulation of the river discharge, at least for the s a l i n i t y fluctuations on the southern section. During ebb-tide, t i d a l currents advect the plume towards the southern section and the slack tide allows maximum ri v e r discharge. For a flood-tide the reverse i s true, so that while the t i d a l currents move the plume northward, the tide i s gradually r e s t r i c t i n g the ri v e r outflow. Thus for the northern section, the two processes oppose each other leading to uncertain s t a t i s t i c a l r e s u l t s . The t i d a l s a l i n i t y amplitudes r e f l e c t the discharge l e v e l . By modifying the entrainment v e l o c i t y expression sp as to make i t dependent on the s t r a t i f i c a t i o n and by reducing the momentum transfer to the plume from the wind, the numerical model can be seen to have the potential to reproduce the long-term fluctuations of the plume caused by the discharge and the wind. This agreement between observations and model results signals two major accomplishments. F i r s t , the Ferry data constitute the f i r s t extensive set of observations that can be readily compared to Stronach's numerical model and be used to ca l i b r a t e i t . The need for c a l i b r a t i o n and v e r i f i c a t i o n was mentioned in Stronach's paper (1981) and again in LeBlond's review (waiting p u b l i c a t i o n ) . Out of two years of Ferry data, only three periods covering a t o t a l of 70 days, received modelling attention. These three periods were a l l characterized by high discharge l e v e l s . There i s s t i l l a large portion of the 1 2 9 data obtained during a somewhat lower l e v e l of discharge, that could be used for further model c a l i b r a t i o n and v e r i f i c a t i o n . Secondly, the fact that the wind is seen for the f i r s t time to have a d e f i n i t e e f f e c t on the plume both in the observations and in the model res u l t s , contradicts previous assumptions according to which the wind influence was neglected. In view of the i n a b i l i t y of the ferry data to properly resolve t i d a l fluctuations, no s i g n i f i c a n t improvement in simulation was expected when t i d a l forcing was added to the numerical model. Nevertheless, results from a simple model including t i d a l forcing reproduced for the southern section s a l i n i t y , r e l a t i v e to the sea-level elevation, the phase relationship expected from the advection of the plume by t i d a l currents. In spite of the large magnitudes of the t i d a l currents, the fluctuations of the plume s a l i n i t y , along the ferry sections, seem to be a superposition of small t i d a l variations and a mean set by wind and discharge. Horizontal d i s t r i b u t i o n s of the plume properties from CTD surveys compared favorably with corresponding numerically obtained d i s t r i b u t i o n s . Improvements in the numerical model are needed to c l a r i f y some of the assumptions introduced herein. The physical processes that determine the variations of the wind factor (F,) s t i l l have to be found. The area covered by the model could be extended to include the region of water exchange with the P a c i f i c Ocean at the northern end of the S t r a i t . This extension might prevent fresh water from getting out of the system at the northern boundary. Modulation of the discharge by the tides i s 1 3 0 often thought to produce successive fronts within the plume. 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