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Observations of small scale distributions of chlorophyll : and related physical parameters in British… Wiegand, Ronald Clive 1976

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OBSERVATIONS CF SHALL SCALE DISTRIBUTIONS OF CHLOROPHYLL AND RELATED PHYSICAL PARAMETERS IN ERITISH COLUMBIA COASTAL HATERS ty RONALD CLIVE HIEGANC E . S c , U n i v e r s i t y of Waterloo, 1970 A T h e s i s Submitted 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 the Degree of Easter o f Science i n the Department of P h y s i c s and The I n s t i t u t e c f Oceanography tie accept t h i s t h e s i s as conforming to the re g u i r e d standard THE UNIVERSITY CF ERI1ISH COLUMBIA A p r i l , 1976 (c) Ronald Clive V/iegand, 1976 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 o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 a n d s t u d y . I f u r t h e r a g r e e 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 c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Oceanography ( P h y s i c s ) The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 D a t e A p r i l 1976 i i ABSTRACT In the s p r i n g of 1973 continuous h o r i z o n t a l measurements w e r e made of temperature, s a l i n i t y , oxygen and c h l o r o p h y l l a. i n B r i t i s h Columbia c o a s t a l waters. The sampling procedure i n v o l v e d a towed pumping system and cn-coard i n s t r u m e n t a t i o n . An e f f o r t i s made to d e s c r i b e the d i s t r i b u t i o n s of the measured parameters with p a r t i c u l a r emphasis cn the s m a l l e r s c a l e s , l e s s than 250 m. To t h i s end, techniques of power s p e c t r a l a n a l y s i s were u t i l i z e d to examine the data. R e s u l t s show t h a t there i s v a r i a b i l i t y i n the nature of the d i s t r i b u t i o n s and that the r e l a t e d n e s s of the parameters i s not c o n s i s t e n t , but th a t cn average d i f f e r e n t experiments show s i m i l a r i t i e s . I t appears that to a l a r g e extent the d i s t r i b u t i o n of c h l o r o p h y l l a_ i n an e s f u a r i n e environment i s r e l a t e d t c p h y s i c a l t r a n s p o r t processes. i i i TABLE CF CONTENTS Paqe ABSTRACT i i LIST OF TABLES . . . . . . . . v LIST OF FIGURES v i ACKNOWLEDGEMENTS . . . . X Chapter I INT8CDUCTION 1 I I INSTRUMENTATION 7 2.1 I n t r o d u c t i o n 7 2.2 S a l i n i t y 9 2.3 Temperature . . . . . . . . . . . . . . . . 13 2.4 Oxygen 17 2.5 C h l o r o p h y l l 21 2.6 V e l o c i t y f l u c t u a t i o n s 26 2.7 Mean v e l o c i t y . . . . . . . . . . . . . . . 26 2.8 S i g n a l p r o c e s s i n g 27 I I I ANALYSIS TECHNIQUE . . . 31 3.1 I n t r o d u c t i o n . . . . . 31 3.2 F o u r i e r t r a n s f o r m a t i o n . . . . . . . . . . 31 3.3 Spe c t r a and coherence 34 3.4 Smoothing and windowing . . . . . . . . . . 38 3.5 S t a t i s t i c a l accuracy . . . . . . . . . . . 42 3.6 Treatment of the data 44 I? RESULTS . . . . . . . . . 46 4.1 I n t r o d u c t i o n 46 4.2 Sampling method 46 4.3 Comment on s t a t i o n a r i t y 54 i v Chapter Page 4.4 D i s c u s s i o n of the data 57 i Indian Arm 5m - June . . . . . . . . . 62 i i Howe Sound 5m - June . . . . . . . . . 79 i i i Georgia S t r a i t 5m - June 90 i v Howe Sound 1m - J u l y 96 v Georgia S t r a i t 1, 3, 5m - J u l y . . . . 104 4.5 Averaging 116 V CONCLUSIONS . . . . . . . . . . . . 130 APPENDIX A - HOT HEDGE RESULTS 134 APPENDIX B - EUTE INLET DATA . . . . . . . . . 140 EEf EBENCES 145 V L I S T OF T A B L E S Table Page I Normalizing f a c t o r s f o r the s p e c t r a . . . . . 6 Q VI F i g u r e LIST CF FIGUBES Page 1 Map showing the g e o g r a p h i c a l l o c a t i o n s of the major study areas . . . . . . . . . . . . . . 6 2 Comparison of r e s u l t s c f oxygen measurements using an oxygen probe and Winkler t i t r a t i o n t echniques 20 3 C a l i b r a t i o n curves f o r the fl u o r o m e t e r . . . . . 25 4 Schematic diagram showing the s i g n a l pathways . . 28 5 Graphs of the gain f a c t o r f o r the pump - hose combination f o r s e v e r a l data runs 48 6 Temperature s p e c t r a f o r the June Indian Arm 5m data . . . . . . . . . . 49 7 Coherence between the inboard and outboard t h e r m i s t o r s f o r the June Indian Arm 5m data . 52 8 Temperature - c h l o r o p h y l l coherences f o r seg-ments of the June Indian Arm 5m data: 4 block segments . . . . . . . . . . . 55 9 Temperature - c h l o r o p h y l l coherences f o r seg-ments of the June Indian Arm 5m data: 8 block segments . . . . . . . . . . . . . 56 10 O r i g i n a l data f o r the June Indian Arm 5m run . . 59 11 C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the June Indian Arm 5a data . . . . . . . . . . . . . . 63 12 Oxygen s p e c t r a f o r the June Indian Arm 5o data with one c a l c u l a t e d from detrended data . . . 64 13 Graphs of block averages f c r c h l o r o p h y l l , s a l i -n i t y , and temperature f o r the June Indian Arm 5m data 68 14 Geographical p l o t of the c h l o r o p h y l l block ave-rages f o r the June Indian Arm 5m data . . . . 70 15 Geographical p l o t of the s a l i n i t y block averages f o r the June Indian Arm 5m data 71 16 Coherences of c h l o r o p h y l l with temperature and s a l i n i t y f o r the June Indian Arm 5m data . . . 72 V X 1 Figure 18 19 20 28 29 30 Page 17 Coherences f o r the other parameters f o r the June In d i a n Arm 5m data . . . . . . . . . . . . . . 73 Discharge of the Indian E i v e r f o r the p e r i o d September 1S56 to September 1959 . . . . . . . 75 A p l o t of the average wind f o r the p e r i o d of i n t e r e s t as measured at l o c o . . 76 Graphs of block averages of c h l o r o p h y l l , s a l i n i -t y , and temperature f o r the June Howe Sound 5m data . . . . . . . . . . . 80 21 Temperature s p e c t r a f o r the June Howe Sound 5m data 82 22 C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the June Howe Sound 5m data . . . . . . . . . . . . . . 83 23 The oxygen spectrum f o r June Hcwe Sound 5B data . . . . . . . . . . . . . . . 84 24 Coherences of c h l o r o p h y l l with temperature and s a l i n i t y f o r the June Hcwe Sound 5m data . . . 86 25 Coherences o f the other parameters f o r the June Howe Sound 5m data . . . . . . . . . . . . . . 87 26 Temperature s p e c t r a f o r the June Georgia S t . 5m data ... 91 27 C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the June Georgia S t . 5m data 92 The oxygen spectrum f o r the June Georgia St. 5m data . 93 C h l o r o p h y l l coherences with temperature and s a l i -n i t y f o r the June Georgia S t . 5m data . . . . 94 Coherences o f the other parameters f o r the June Georgia S t . 5a data 95 31 Graphs of bl o c k averages of c h l o r o p h y l l , s a l i n i -t y , and temperature f o r J u l y Hcwe sound 1m data 97 32 Temperature s p e c t r a f o r the J u l y Hcwe Sound 1m data 98 33 C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the J u l y Howe Sound 1m data 99 v i i i The oxygen spectrum f o r the J u l y Hcwe Sound 1a 35 Coherences o f c h l o r o p h y l l with temperature and s a l i n i t y f o r J u l y Howe Sound 1m data . . . . . 102 36 Coherences of the other parameters f o r the J u l y Howe Sound 1a data . . 103 37 Geographical p l o t of c h l o r o p h y l l block averages f o r the J u l y Howe Sound 1a data . . . . . . . 105 38 Geographical p l o t of s a l i n i t y block averages f o r the J u l y Howe Sound 1a data . . . . . . . . . 106 39 Spectra f o r J u l y Georgia St. 1a data 108 40 Coherences f o r J u l y Georgia S t . 1a data . . . . . 109 41 Spectra f o r J u l y Georgia S t . 3a data . . . . . . 110 42 Coherences f o r J u l y Georgia S t . 3m data . . . . . 111 43 Spectra f o r J u l y Georgia S t . 5a data 112 44 Coherences f o r J u l y Georgia S t . 5m data . . . . . 113 45 Graphs o f c h l o r o p h y l l and s a l i n i t y block averages f o r the J u l ; Georgia S t . data 115 46 C h l o r o p h y l l coherences with t e a p e r a t u r e and s a l i -n i t y f o r 10 J u l y data runs i n d i v d u a l l y p l o t t e d 118 47 Averages - the t e a p e r a t u r e s p e c t r a f o r the lon g e r data runs . . . . . . . . . . . . . . . 121 48 Averages - the s a l i n i t y and c h l o r o p h y l l spec-t r a f o r the longer data runs . . . . . • . . . 122 49 Averages - the oxygen spectrum f o r the longer data runs . . . . . . . . • . • 123 50 Averages - c h l o r o p h y l l coherences with teapera-t u r e and s a l i n i t y f o r the lon g e r data runs . . 124 51 Averages - coherences f o r the other parameters f o r the l o n g e r data runs . . . . . . . . . . . 127 52 Spectra f o r A p r i l Indian Arm 3a data i n c l u d i n g the hot wedge . . . . 136 i x F i gure Page 53 Hot wedge coherences f o r the A p r i l I n dian Aria 3a data . . . . . . . . . . . . . . . . . . . 137 54 Spectra f o r A p r i l Indian Arm 5m data i n c l u d i n g the hot wedge . . . . . . . . . . . . . . . . 138 55 Hot wedge coherences f o r the A p r i l Indian Arm 3m data . . . . . 139 56 Spectra f o r Hay Bute 1m data 142 57 Spectra f o r May Bute 3m data . . . . . . . . . . 143 58 C h l o r o p h y l l coherences with temperature and s a -l i n i t y f o r Bay Bute 1, 3, and 5a data . . . . 144 X ACKNOWLEDGEMENTS The l a b o u r t h a t went i n t o producing t h i s p a r t i c u l a r work was shared by many people. F i r s t l y I should l i k e t o express my g r a t i t u d e t o my s u p e r v i s o r Dr. Stephen Pond, who p a t i e n t l y guided me to the completion of t h i s t h e s i s . The design and c o n s t r u c t i o n of the apparatus p r i n c i p a l l y i n v o l v e d Mr. David E n g l i s h , Hr. Heinz Heckl and Mr. Edward Meyer, a l l of the I n s t i t u t e of Oceanography. The experiments were c a r r i e d out with the a i d of C a p t a i n S c a n l i n and the o f f i c e r s and crew o f the C.S.S. Vector. For able a s s i s t a n c e and spending some long n i g h t s c f data a c q u i s i t i o n with me I thank Br. Bon Johnson and Mr. Peter Merchant. Ms. Grace Kamitakahara a s s i s t e d me with the computing t h a t was necessary. I would a l s o l i k e t o thank Dr. T. B. Parsons f o r h i s s u q g e s t i o n s and Drs. B. W. B u r l i n g and P. H. Leblond f o r t h e i r comments on the manuscript. My c o n v e r s a t i o n s with other f a c u l t y and students of the I n s t i t u t e have a l s o b e n e f i t t e d me. In a d d i t i o n I thank fls. C a r o l Norberg f o r t y p i n g the manuscript. During my years of study at the I n s t i t u t e of Oceanography I was p e r s o n a l l y supported by two NBC postgraduate s c h o l a r s h i p s and by NBC grant 67-8301. The i n i t i a l purchase of eguipment was made p o s s i b l e through the P r e s i d e n t ' s Besearch Fund grant EME 67-5057. A d d i t i o n a l r e s o u r c e s d u r i n g the a n a l y s i s of the data came from NBC grant 67-8301. 1 CHAPTER I INTRODUCTION 8 i t h i n the l a s t few yea r s , there has been a renewed i n t e r e s t i n the d i s t r i b u t i o n of phytoplankton i n the oceans. I t i s w e l l known t h a t , i n g e n e r a l , plankton e x h i b i t s p a t i a l h e t e r o g e n e i t y or p a t c h i n e s s and the d e s i r e i s to d e s c r i b e t h i s phenomenon and i f p o s s i b l e a t t r i b u t e i t t o some c a u s a l mechanisms. One reason f o r doing so i s the importance o f p l a n t l i f e i n the marine food c h a i n ; indeed p l a n t s are the primary l e v e l . I t i s now thought t h a t h e t e r o g e n e i t y i s , a t l e a s t t o some ex t e n t , r e s p o n s i b l e f o r the s t a b i l i t y o f the system ( S t e e l e , 1974). The value of bioaass e s t i m a t e s r e s u l t i n g from d i s c r e t e sampling techniques must a l s o be reviewed. C o n s i d e r i n g the s p a t i a l v a r i a t i o n s d i s p l a y e d by other commonly measured o c e a n i c p a r a a e t e r s , t h e r e i s no "3* p r i o r i reason f o deduce a uniform phytoplankton p o p u l a t i o n as being the usu a l s t a t e and probably the o p p o s i t e i s a much more tenable h y p o t h e s i s . Phytoplankton can have many r e s t r i c t i o n s imposed on them by the nature of t h e i r environment. The d i s t r i b u t i o n can be a f f e c t e d by t e a p e r a t u r e or s a l t boundaries; t h e i r growth depends on the a v a i l a b i l i t y of n u t r i e n t s and l i g h t ; they o f f e r only p a s s i v e r e s i s t a n c e t o the no t i o n o f t h e i r environment. A l l of these f a c t o r s can l e a d to an inhomogeneous phytoplankton crop. B a i n b r i d g e (1957) has reviewed the l i t e r a t u r e on plankton p a t c h i n e s s and f i n d s the e a r l i e s t d e s c r i p t i o n s r e s u l t e d from the ob s e r v a t i o n s of s e a f a r e r s and n a t u r a l i s t s . James Cook (1815) on h i s i n i t i a l voyage w r i t e s i n h i s d i a r y : "On the n i n t h an amazing number of atoms were taken out of the s e a . These were of a y e l l o w i s h c o l o u r and few of them were more than the f i f t h p a r t of an inch l o n g . . . . The sea was t i n g e d i n such a manner as to e x h i b i t broad s t r e a k s of a s i m i l a r c o l o u r f o r near the space of a mile i n length and f o r s e v e r a l hundred yards i n breadth." While cn board the Beagle, C h a r l e s Darwin (1952) saw " s t r i p s of dark y e l l o w i s h , or mud-like water; these s t r i p s were some miles l o n g , but only a few yards wide, and they were separated from the surrounding s u r f a c e by a sinuous yet d i s t i n c t margin." As f o r the cause o f these s t r i p s he i n c l u d e s , " C a p tain C o l n e t t remarks...that the d i r e c t i o n o f t h e bands i n d i c a t e s t h a t c f the c u r r e n t s ; i n the d e s c r i b e d case, however, the l i n e was caused by the wind." P o s s i b l y he i s d e s c r i b i n g what today are c a l l e d windrows, r e s u l t i n g from the c i r c u l a t i o n set-up i n the ocean under l i g h t winds: Langmuir c i r c u l a t i o n . F u r t h e r on i n h i s d i a r y Darwin mentions " c i r c u l a r and o v a l patches, from two to f o u r yards i n diameter." These were a t depths g r e a t e r than 4 metres because the Beagle, which had a draught of 13 f e e t c o u l d s a i l d i r e c t l y over these patches without d i s t u r b i n g them. In s p i t e of these and many other s u r f a c e o b s e r v a t i o n s of p a t c h i n e s s , many people s t i l l b e l i e v e d t h a t i n g e n e r a l , the plankton d i s t r i b u t i o n c ould be d e s c r i b e d as uniform. And duri n g the beginning of t h i s century t h e r e was c o n t r o v e r s y concerning the accuracy of biomass e s t i m a t e s made from the r e s u l t s of d i s c r e t e sampling (Hardy, 1935). That h e t e r o g e n e i t y , not u n i f o r m i t y , i s more usual was p a r t i a l l y e s t a b l i s h e d by the work of Herdmann (1907), who i n making net hauls was made aware of both temporal and s p a t i a l v a r i a b i l i t i e s i n the plankton community. F u r t h e r proof came with the i n v e n t i o n of the Hardy plankton r e c o r d e r which i s towed through the water and f i l t e r s c o n t i n u o u s l y ; the samples being caught i n a f i n e s i l k mesh which t r a v e r s e s the sampling o r i f i c e a t a known r a t e . R e s u l t s of tows a c r o s s the North Sea (Lucas,1941) showed l a r g e s c a l e s p a t i a l v a r i a b i l i t y i n the abundance of many p h y t o p l a n k t e r s . There are drawbacks t o t h i s type of sampling however, not the l e a s t being the amount of work necessary t o reduce the data. Moreover the r e s u l t s are one-dimensional and l i m i t e d i n r e s o l u t i o n . However i t would seem that the idea of plankton p a t c h i n e s s was now well e s t a b l i s h e d . Most i n v e s t i g a t i o n s became concerned with the v a r i a b i l i t y i n the zooplankton p o p u l a t i o n , e s p e c i a l l y the d i f f e r e n c e s i n s p e c i e s content of s u c c e s s i v e h a u l s . Some of t h i s v a r i a n c e was no doubt the r e s u l t o f f i l t e r i n g d i f f e r e n t q u a n t i t i e s of water as might occur using n e t s , and g r a d u a l l y pumps came i n t o use. Now the amount of water f i l t e r e d c o u l d be e x a c t l y determined and the v a r i a n c e encountered d u r i n g sampling c o u l d be a s c r i b e d to the p o p u l a t i o n (Barnes and M a r s h a l l , 1951). attempts were made at producing d i s t r i b u t i o n models f o r plankton and to account f o r the patches u s i n g environmental parameters ( C a s s i e , 1963). But as s t a t e d above the biomass was being d i s c u s s e d t a x o n o m i c a l l y and not i n i t s t o t a l i t y . The most r e c e n t s t u d i e s o f phytoplankton abundance have concerned themselves again with the t o t a l d i s t r i b u t i o n . T h i s i s p a r t i a l l y the r e s u l t of technique s i n c e c h l o r o p h y l l a i s measured and i t i s g e n e r a l l y c o n s i d e r e d to be an index of the t o t a l crop. C h l o r o p h y l l £ has the property t h a t i t f l u o r e s c e s and i n s t r u m e n t a t i o n has been de v i s e d to measure t h i s f l u o r e s c e n c e . With proper c a l i b r a t i o n ( S t r i c k l a n d , 1968; Lorenzen, 1966) the technique can be used t o measure the amount of i n v i v o c h l o r o p h y l l . S t u d i e s o f the l a r g e s c a l e d i s t r i b u t i o n of c h l o r o p h y l l have f e a t u r e d a r e l a t i o n s h i p with hydrographic parameters (Lorenzen, 1971; P i a t t , D i c k i e , and T r i t e s , 1970) but perhaps most i n t r i g u i n g i s the hypothesis of a c o u p l i n g between the phytoplankton d i s t r i b u t i o n and t h a t of t u r b u l e n t energy ( P i a t t , 1972; Denoan and P i a t t , 1974). These l a s t two r e f e r e n c e s present data i n which the v a r i a n c e spectrum of c h l o r o p h y l l a, demonstrates a k - s / 3 behaviour c h a r a c t e r i s t i c of homogeneous i s o t r o p i c t u r b u l e n c e . Using temperature as an " i n d i c a t o r " of the t u r b u l e n t t r a n s p o r t processes, Denman and P i a t t (1974) i n f e r from high values over c e r t a i n s c a l e s i n the c h l o r o p h y l l - t e m p e r a t u r e coherency spectrum, t h a t the d i s t r i b u t i o n of c h l o r o p h y l l i s l a r g e l y determined by p h y s i c a l r a t h e r than b i o l o g i c a l processes f o r these s c a l e s . I n t h i s t h e s i s , the s p a t i a l h e t e r o g e n e i t y of the* phytoplankton biomass i s examined i n the s u r f a c e r e g i o n o f an e s t u a r i n e environment. In a d d i t i o n t o c h l o r o p h y l l a, temperature, s a l i n i t y , oxygen, v e l o c i t y and f o r some cases v e l o c i t y f l u c t u a t i o n s were measured. Data were c o l l e c t e d i n three i n l e t s , I n d i a n Arm, Howe Sound and Bute as w e l l as i n Georgia S t r a i t , i n the v i c i n i t y of the F r a s e r River plume, and a t t h r e e depths corresponding approximately t o 1, 3, and 5 metres. The l o c a t i o n s ( f i g . 1) were v i s i t e d d u r i n g the months of A p r i l through J u l y 1973, roughly c o i n c i d i n g with the s p r i n g phytoplankton bloom and i t s d e c l i n e . Bute I n l e t was the s u b j e c t of only one experiment, i n Hay. The o t h e r s were a l l s t u d i e d dur i n g the same week a t approximately one month i n t e r v a l s . The Bute data were obtained with the s h i p a t anchor whereas normally the s h i p was i n motion while sampling was t a k i n g p l a c e . BUTE INLET f i g . 1: A map showing the geographical l o c a t i o n s of the study areas. 7 CHAPTER I I INSTRUMENTATION 2.1 I n t r o d u c t i o n A general d e s c r i p t i o n o f sampling procedure w i l l be gi v e n , f o l l o w e d by d e s c r i p t i o n s o f the i n d i v i d u a l sensing d e v i c e s . B r i e f l y , water at a given depth was pumped on board s h i p where temperature, oxygen, s a l i h i t y and c h l o r o p h y l l ware measured. In a d d i t i o n , temperature, v e l o c i t y f l u c t u a t i o n s and mean v e l o c i t y were measured i n s i t u . Sampling was done using a 0.5 hp., s i x - s t a g e submersible deep w e l l pump, p a r t s of which were coated i n r u s t - i n h i b i t i n g p a i n t t o reduce c o r r o s i o n . The pump, the hose and c a b l e s t o the i n s i t u instruments were housed i n a 10 cm aluminum tube with p o r t a l s c u t i n t h i s tube to access the pump i n t a k e and t c allow the c a b l e s t o be at t a c h e d t o the instruments. Any underwater conn e c t i o n s were made w a t e r t i g h t through l i b e r a l use of s e l f -v u l c a n i z i n g rubber tape, h e l d i n p l a c e by bl a c k v i n y l e l e c t r i c i a n s tape. A cage or basket surrounding the pump i n t a k e and the underwater instruments, was attached as p r o t e c t i o n during use and during i n s t a l l a t i o n and removal. The design was such as t o minimize i n t e r f e r e n c e with the o p e r a t i o n of the instruments yet r e t a i n s u f f i c i e n t s t r e n g t h . T h i s e n t i r e package, which w i l l sometimes be r e f e r r e d t o as the boom, was allowed to s l i d e through a c o l l a r which i n turn 8 was a t t a c h e d t o the forward crane o f the r e s e a r c h v e s s e l C.S.S. Vect o r . The hook and p u l l e y system of the crane allowed the r a i s i n g o r l o w e r i n g o f the apparatus t o the d e s i r e d depth, and i t s a r t i c u l a t i o n allowed the removal of the boom and i t s placement on board s h i p when not i n use. To f u r t h e r ensure minimum v e r t i c a l or r o t a t i o n a l motion of the instrument package, the c o l l a r c o n t a i n e d a s e t screw which was t i g h t e n e d a g a i n s t the boom. Depth r i n g s were marked on the boom i n one metre i n t e r v a l s and proper forward o r i e n t a t i o n of the sensors was a s c e r t a i n e d v i s u a l l y with l i t t l e e r r o r i n v o l v e d . The forward crane was used as i t enabled placement of the boom o u t s i d e of t h e s h i p ' s bow wave, thereby minimizing the e f f e c t s of the s h i p ' s wake on the measurements. During the experiments (except i n Bute) the s h i p attempted t o maintain speed at about 100t 20 cm/sec (2 k n o t s ) . Since the pumped water had a speed i n the hose of about 200 cm/sec, a l l the s t r u c t u r e present c o u l d be sampled. Black, rubber s a n d b l a s t hose was used to t r a n s p o r t the water on deck. The hose was approximately 30 m i n l e n g t h and had 1 cm w a l l s with a 2 cm o r i f i c e . I t s i n t e r i o r was smooth so as not to f u r t h e r i n c r e a s e mixing. However the pump i s an e x c e l l e n t a g i t a t o r and the flow i n the hose appeared f u l l y t u r b u l e n t . The w a l l t h i c k n e s s was chosen t o reduce heat t r a n s f e r . Opague hose was chosen s i n c e p r e v i o u s experiments with t r a n s p a r e n t garden hose had shown the hose to a c t as a l i g h t pipe which s e r i o u s l y a f f e c t e d the o p e r a t i o n of the fl u o r o m e t e r . The onboard instrument-holder c o n t a i n i n g temperature, oxygen and s a l i n i t y probes was fa s h i o n e d out of t r a n s p a r e n t a c r y l i c p l a s t i c . A i m s e c t i o n of hose was placed between t h i s holder and the f l u o r o a e t e r so t h a t l i g h t e n t e r i n g the system here would not a f f e c t the measurement of c h l o r o p h y l l . Transparent a c r y l i c was chosen f o r the hol d e r so t h a t the sensors c o u l d be monitored f o r f o u l i n g . The c r o s s - s e c t i o n a l area a f f o r d e d the fl o w i n the p l a s t i c h o l d e r was the same as tha t i n the rubber hose. 2.2 S a l i n i t y S a l i n i t y was measured with a Yellow Springs Instrument Co. (Y.S.I.) model 33 S-C-T meter and probe. In order t o measure c o n t i n u o u s l y , a connection was made to the l e a d s o f the instrument' 1 s meter; the s i g n a l used was the v o l t a g e a c r o s s the meter which was s u i t a b l y a m p l i f i e d before r e c o r d i n g . Because the next stage i n s i g n a l c o n d i t i o n i n g had a very high i n p u t impedance, t h i s procedure was u n l i k e l y t o l o a d down the meter. The probe was h e l d i n p l a c e i n the holder using a s e t screw and although the c l e a r a n c e between the probe and h o l d e r was l e s s than the recoaaendations of the manufacturer, c a l i b r a t i o n checks showed t h a t t h e r e were no measureable e f f e c t s . Sea water, a p p r o p r i a t e l y d i l u t e d , was used t o c a l i b r a t e the instrument using the s a l i n i t y as determined by an Autolab model 601 i n d u c t i v e s a l i n o m e t e r as a r e f e r e n c e . The voltage s i g n a l r e c e i v e d from the s a l i n o m e t e r was not always t r u l y r e p r e s e n t a t i v e of the s a l i n i t y of the sample. The probe a c t u a l l y measures e l e c t r i c a l c o n d u c t i v i t y and a 10 temperature c o r r e c t i o n must be a p p l i e d t o o b t a i n s a l i n i t y , from the s i g n a l r e c e i v e d from the probe. The model 3 3 does not have automatic compensation but the c o r r e c t i o n i s a p p l i e d manually which can not be done duri n g sampling. A c o r r e c t i o n was a p p l i e d a t the s t a r t of each run but t h i s would not always be adeguate; the c o r r e c t value of s a l i n i t y would be measured o n l y when the temperature of the sample was the same as t h a t of the compensation. I t was decided t o make f u r t h e r c o r r e c t i o n s using the temperature s i g n a l s o b t a i n e d . To determine a r e l a t i o n s h i p between s a l i n i t y , c o n d u c t i v i t y and temperature, data were f i t t e d t o the polynomial S = k,C + kjT + kjCT + k^C* + lyT* + k tG lT + k^CT* 2.2.1 S i n % 0 ; T in*C ; C in H f 4 mhos. The C 3 and T 3 terms i n the expansion were not necessary f o r a good f i t and were omitted. The data were taken from the Handbook of Oceanographic Tables and r e g r e s s i o n a n a l y s i s performed to e v a l u a t e the c o e f f i c i e n t s . The f o l l o w i n g v a l u e s were o b t a i n e d f o r the c o e f f i c i e n t s , where the format of EfcOx has been used t o des i g n a t e 10 to the * x+l* power. ' k, = 0.1085 k^ = 0.1715E-02 k t = -0.0427 k 4 = -0.1119E-05 k 3 = -0.3201E-02 k f = 0.5097E-04 k^ = 0.4075E-04 One i s i n t e r e s t e d i n the r o l e of products of f l u c t u a t i o n s i n c o n d u c t i v i t y and temperature i n determining the f l u c t u a t i o n s i n s a l i n i t y . By w r i t i n g the parameters as the sum of a mean and 11 a p e r t u r b a t i o n and s u b s t i t u t i n g i n eguation 2.2.1, the terms i n v o l v i n g products of f l u c t u a t i o n s are shown to be: i) k 3(Al*C) i i ) k 4(AC) Z i i i ) k^AT) 2 , iv) k 4(T(Acf + 2CACAT + Gtff AT) v) k^(C(aT) X + 2TACAT + UT?AC) . Suppose we had a t e a p e r a t u r e f l u c t u a t i o n of > 1.0 C*about a mean o f 10*C and a + 20 x 10"* mhos c o n d u c t i v i t y f l u c t u a t i o n about a mean of 200 x 10-* mhos. These would be extreme v a l u e s f o r the data. The numerical e v a l u a t i o n of the terms above g i v e s : 9 -6.40E -02 ( 3% )" i i ) 1.63E -02 (0.8%) i i i ) 1.72E -03 (0.08%) iv) -1.39E. -02 (0.6%) v) 3.16E--02 (1.5%) where the percentage i n brackets r e p r e s e n t s the r a t i o of the higher order f l u c t u a t i o n to the l i n e a r c o n d u c t i v i t y term. The c o n t r i b u t i o n s from the l i n e a r terms would be 2.17 from the c o n d u c t i v i t y term and -4.27 x 10- 2 (2%) f r o a the t e a p e r a t u r e term. In t h i s case we can n e g l e c t a l l the h i g h e r order terms and the l i n e a r temperature term as w e l l . N e g l e c t i n g the h i g h e r order terms even though the k^and k^terms are of the same order as the l i n e a r temperature term, leads to an e r r o r of about 37« to 5% . Eut i f the temperature f l u c t u a t i o n s remain l a r g e and the changes i n c o n d u c t i v i t y become s m a l l e r , 1% f o r example, then the l i n e a r temperature term becomes important (20% of the l i n e a r c o n d u c t i v i t y term) while the h i g h e r order terms may s t i l l be n e g l e c t e d . The v a l u e s of the terms i n t h i s case are: i) -6.40E-03 ( 3% ) i i ) 1.63E-04 (0.08%) i i i ) 1.72E-03 (0.8%) iv) -9.44E-04 (0.4%) v) 1.23E-02 (5.7%) Because temperature f l u c t u a t i o n s o f t h i s magnitude were seldom encountered with s m a l l s a l i n i t y f l u c t u a t i o n s , and t h e r e f o r e the k^. term would seldom be as l a r g e as 6% of the l i n e a r c o n d u c t i v i t y term, only the l i n e a r temperature term was c o n s i d e r e d important and c o r r e c t i o n s made f o r i t s c o n t r i b u t i o n s . Because the instrument c o u l d not compensate f o r f l u c t u a t i o n s i n temperature about t h e manually s e t compensation value, the data recorded would be a f u n c t i o n of temperature and wa can write the value of s a l i n i t y as a T a y l o r s e r i e s expansion about the manually set value T 0: S = S(TV) + dSl (T - To) + d^ SJ ( T - T 0 f + . . . 2.2.2 For s m a l l temperature f l u c t u a t i o n s ( d 2 S / d T 2 ) . ( A T ) 2 z<(dS/dT)« ( A T ) and t h e r e f o r e the higher order terms can be dropped from the e x p r e s s i o n . Because v a r i a n c e i n v o l v e s d i f f e r e n c e s from a mean value i t i s convenient t o express the temperature dependence i n terms of the mean temperature r a t h e r than the compensation value, 13 S(T C) = S(T^) - dSj ( T ^ - 7^ ) 2.2.3 3T1 To where the d i f f e r e n c e Between T* v and T» w i l l be s m a l l i n the data i n most i n s t a n c e s . Therefore we can write S = S(T* V) + dSl ( T - V ) 2 2 4 where the term d S / d T l T (T- T a V ) r e p r e s e n t s the f l u c t u a t i o n s i n the data due to temperature changes which must be removed. Si n c e the F o u r i e r c o e f f i c i e n t spectrum i s r e p r e s e n t a t i v e of the q u a n t i t y (T - T ^ ) , any o p e r a t i o n s may be performed on the c o e f f i c i e n t s r a t h e r than the o r i g i n a l data provided these o p e r a t i o n s are l i n e a r . The response of the s a l i n o m e t e r i n our case i s mainly determined by the f l u s h i n g time o f t h e sensor head although i t w i l l be a l t e r e d as the e l e c t r o d e s f o u l . Hhen f o u l i n g was d i s c o v e r e d d u r i n g the course of the experiment the probe was cleaned. The l e n g t h of the sensing head i s 5 cm. With the v e l o c i t y of the flow i n the system being about 200 cm/sec, the f l u s h i n g time i s much l e s s than 1 second, the approximate c u t -o f f freguency f o r the f i l t e r s used and so we would expect the s a l i n i t y data to be good f o r the e n t i r e range of f r e g u e n c i e s examined. However, the smoothing e f f e c t s of the pumping system w i l l cause d i f f e r e n c e s from the i n s i t u f l u c t u a t i o n s a t the higher f r e g u e n c i e s as we s h a l l see. 2.3 Temperature I t was decided to measure temperature i n two p l a c e s , a t the pump i n t a k e and i n the instrument h o l d e r on board. In t h i s way 14 the t r a v e l time of the water from pump to instrument c o u l d be determined as w e l l as some of the e f f e c t s of pumping the water through the hose. By comparing s p e c t r a l shapes and computing coherence and phase, the amount of mixing or smoothing and the l o s s of frequency response can be estimated. T h e r m i s t o r s were used as temperature t r a n s d u c e r s . They are not extremely f r a g i l e and are h i g h l y temperature s e n s i t i v e . F r a g i l i t y must be c o n s i d e r e d a f a c t o r i n d e c i d i n g the type of sensor when i t i s placed i n waters which are abundant with plankton. The type used f o r t h i s experiment were Fenwall E l e c t r o n i c s Inc. type GB41P2 g l a s s bead t h e r m i s t o r s and ware c a l l e d macrobeads because of t h e i r s i z e . Although use of microbead t h e r m i s t o r s would have i n c r e a s e d the freguency response, t h i s was not necessary because of the l o n g e r time c o n s t a n t s of the oth e r instruments. The r e s i s t a n c e s of the t h e r m i s t o r s were about 11 K ohms f o r a temperature of 20°C. For use d u r i n g t h i s experiment, both were mounted by p o t t i n g the base i n a p l a s t i c tube with epoxy. The t h e r m i s t o r s were used as one arm of a Hheatstone bridge which had another arm (R c) t h a t c o u l d be c o n t r o l l e d manually. 3y having the other r e s i s t o r s (R) i n the bridge very l a r g e and equa l , the output f o r the brid g e may be w r i t t e n as: v O O T -|| T-^o» 2 - 3 > 1 where Vg r e p r e s e n t s the supply v o l t a g e . In o p e r a t i o n , the value of R e was ad j u s t e d so t h a t i t would approximately balance the bridge when R T was r e p r e s e n t a t i v e of the t h e r m i s t o r r e s i s t a n c e at the average value of temperature. 15 T h i s value r e p r e s e n t s the n o n - o s c i l l a t i n g or d.c. l e v e l of the temperature s i g n a l and i s r e f e r r e d to as an o f f s e t . Both t h e r m i s t o r s were c a l i b r a t e d s i m u l t a n e o u s l y i n the same temperature bath, using a raercury-in-glass thermometer as a r e f e r e n c e . The l a t t e r c o u l d be read to the nearest 0.0 5 C* A t e m p e r a t u r e - r e s i s t a n c e r e l a t i o n was determined by l e a s t sguares f i t t i n g the data p o i n t s to an e x p o n e n t i a l of the form T ~ K e 2.3.2 I t i s more usual to f i t the data to the standard t e m p e r a t u r e - r e s i s t a n c e r e l a t i o n R = R 0 e 2.3.3 but the former was convenient and the f i t very good, the rms. e r r o r i n the constants being l e s s than 151. A v o l t a g e - r e s i s t a n c e r e l a t i o n s h i p was found by f i t t i n g data p o i n t s t o the l i n e R«T = R Q+ mV 2.3.4 with l e s s than 0.1% e r r o r i n R and m. S u b s t i t u t i o n i n t o the temperature eguation g i v e s T = ke* ( where k = Ke **• ; k = k,m ). 2.3.5 Expanding t h i s as a T a y l o r s e r i e s and s u b t r a c t i n g T from both s i d e s t o get an eguation f o r the f l u c t u a t i o n s T = dT(AV) + 1 d^TUvf + ... 2.3.6 dV 2 which upon s u b s t i t u t i o n g i v e s T = k'ke*' V < w (AV) + 1 k ' ^ k e ^ C A V ) * = k*T M(AV) + 1 k'^TavCftV). 2.3.7 2 Because the v a r i a t i o n s i n temperature are not l a r g e so that*V i s small and because k'/2 i s about 0.05, only the l i n e a r term need be kept and the eguation f o r the temperature f l u c t u a t i o n s i s A T = k \ v ( A V ) 2.3.8 The c a l i b r a t i o n f a c t o r then i s k*T a v which i s determined f o r each data s e t . The response of the t h e r m i s t o r s i n s t i l l water was e m p i r i c a l l y determined to be about 2 seconds f o r an approximate 90% change which corresponds to a time constant of about 1 second. For such a time constant the amplitude of the f l u c t u a t i o n s i s 71% of the a c t u a l value at 1/{2TT x time constant) = 0.16 Hz. The time constant i s changed when t h e r e i s f o r c e d c o n v e c t i o n which i n t u r n i s dependent on the Reynolds number of the flow. With the flow r a t e of about 200 cm/sec and a l e n g t h s c a l e of the s i z e of the t h e r m i s t o r , the time constant of the t h e r m i s t o r s w i l l be improved by about a f a c t o r c f 10. T h i s improvement i s l i k e l y to be a f f e c t e d by the nature o f the c o n s t r u c t i o n of the t h e r m i s t o r s i n c e the a c t u a l semi-conductor m a t e r i a l i s coated with g l a s s , and the f a c t o r of 10 c o u l d be an over-estimate. From the r e s u l t s presented l a t e r i t appears that the e f f e c t i v e time constant i s about 1/3 sec and the temperature s i g n a l should be good over most of the range of f r e q u e n c i e s i n which w<= are i n t e r e s t e d . 17 2.4 Oxygen D i s s o l v e d oxygen c o n c e n t r a t i o n was measured with a YSI model 54 oxygen meter and number 5419 oxygen-temperature probe. For continuous r e c o r d i n g , the volt a g e a c r o s s the meter, a f t e r s u i t a b l e a m p l i f i c a t i o n , was used. The manufacturer s t a t e s t h a t the probe has a pressure e g u a l i z a t i o n device which e l i m i n a t e s e r r o r s caused by deep water pressures, a i r bubbles i n s i d e the probe, and i n t e r n a l pressures caused by thermal g r a d i e n t s . The probe i s a C l a r k type p o l a r o g r a p h i c sensor; the e l e c t r o d e s being immersed i n a KC1 s o l u t i o n and separated from the environment with a T e f l o n membrane. The membrane i s permeable to oxygen with the d i f f u s i o n r a t e being determined by the d i f f e r e n c e i n pressure from the o u t s i d e to the i n s i d e of the c e l l . Since oxygen i s reduced almost immediately at the cathode, the d i f f u s i o n w i l l be r e l a t e d to the p a r t i a l pressure of oxygen i n the surrounding medium. I t i s important t h a t the f l u i d near the membrane be c o n t i n u a l l y r e p l a c e d s i n c e otherwise the d i f f u s i o n l a y e r w i l l extend beyond the membrane and cause abnormally low re a d i n g s but t h e r e should be no problem i n the experimental s e t -up because of the f l u s h i n g r a t e . Temperature, which a f f e c t s the s o l u b i l i t y of oxygen i n water and a l s o the membrane, i s measured by the probe and s u i t a b l e compensation i s a p p l i e d e l e c t r o n i c a l l y . D n f o r t u n a t e l y no automatic compensation i s a v a i l a b l e f o r the e f f e c t s o f s a l i n i t y which although not g r e a t , do change the rea d i n g . The presence of s a l t i n water lowers the s o l u b i l i t y of oxygen. For example a t 10°C the s a t u r a t i o n value of oxygen i s r e l a t e d t o s a l i n i t y by 18 Oj_ = 7.8 - 0.046S ( O t i n ml/1 ; S i n % 0 ) 2.4.1 C a l i b r a t i o n was done i n the f o l l o w i n g manner. Before use, the meter was s e t to a c e r t a i n value i n a i r of a c e r t a i n temperature. The v o l t a g e corresponding t o t h i s meter reading was then set equal t o the s a t u r a t i o n value of oxygen i n water at the recorded temperature, and of a s a l i n i t y equal t o the averaqe s a l i n i t y of the data. A p r o p o r t i o n a l r e l a t i o n s h i p between oxygen and voltage was assumed s i n c e the meter s c a l e and the meter s c a l e v o l t a g e r e l a t i o n s are l i n e a r . In some i n s t a n c e s , the v a r i a t i o n s i n the oxygen f i e l d were s m a l l , of the same order as those caused by f l u c t u a t i o n s i n the s a l i n i t y f i e l d . T h erefore a c o r r e c t i o n was a p p l i e d to the oxygen data, using the r e l a t i o n h i p given above. The c o e f f i c i e n t 0.046 was found not t o vary s i g n i f i c a n t l y . A c o r r e c t i o n f o r the e f f e c t s of membrane d r i f t was a l s o a p p l i e d . In some i n s t a n c e s readings were taken a f t e r use and the percentage degradation determined by comparison with the i n i t i a l c a l i b r a t i o n s . T h i s d e g r a d a t i o n was assumed to be a l i n e a r process i n time and a s u i t a b l e c o r r e c t i o n was made to the gain f a c t o r to account f o r the change. The c o r r e c t i o n was made to the g a i n and not simply the d.c. l e v e l s i n c e membrane de g r a d a t i o n a l t e r s the d i f f u s i o n r a t e f o r the same p a r t i a l p r e s s u r e . A t y p i c a l value of degradation i s 3.5£1% per hour of use and i t was t h i s value t h a t was used when no a f t e r - u s e c a l i b r a t i o n checks were a v a i l a b l e . The mean valu e s obtained by such procedures are compared to va l u e s r e s u l t i n g from Winkler t i t r a t i o n s of d i s c r e t e samples 19 taken a t approximately the same time and depth. The H i n k l e r values were o f t e n only s i n g l e samples and c e r t a i n l y not distance-averaged v a l u e s . A comparison i s shown i n f i g u r e 2 with the s t r a i g h t l i n e r e p r e s e n t i n g a match i n v a l u e s . This comparison suggests t h a t the oxygen probe does measure the oxygen c o n c e n t r a t i o n q u i t e w e l l . There i s only one p o i n t f a r o f f the match l i n e and i t i s p o s s i b l y the r e s u l t of a f a u l t y t i t r a t i o n or an anomalous value because of the d i s c r e t e sampling technique used t o o b t a i n the samples f o r t i t r a t i o n . The response of the oxygen probe i s dependent on the d i f f u s i o n time of the gas through the membrane. T h i s assumes inst a n t a n e o u s r e d u c t i o n at the cathode w i t h i n the c e l l . I f we f u r t h e r assume t h a t the membrane i s not an important impedance, then the l i m i t i n g f a c t o r w i l l be the oxygen d e f i c i e n t boundary l a y e r which i s b u i l t up around the membrane when c i r c u l a t i o n i s inadequate. T h i s i s not c o n s i d e r e d to be a problem i n t h i s experiment. Another f a c t o r which might determine response i s the s t a t e of c l e a n l i n e s s of the cathode. No e m p i r i c a l d e t e r m i n a t i o n of the time c o n s t a n t was done because of lac k of f a c i l i t i e s t o do i t adequately, but judging from the r e s u l t s of the N a t i o n a l Oceanographic Instrumentation Centre (NOICC, 1972) t e s t s of other s i m i l a r probes - Beckman Model 735 and Minos Dom - the 1 time c o n s t a n t w i l l be about 7 or 8 seconds. They, a l s o show t h a t the time constant i s temperature s e n s i t i v e , the 7 or 8 seconds quoted i s f o r a 10 °C temperature whereas at 15°C the response has improved to 5 seconds f o r the model 7 35. They do not mention how they measure the time constant but i n a t e s t o f another oxygen a n a l y z e r - the I o n i c s 20 ml./ I. f i g . 2: A comparison of oxygen values obtained using the oxygen probe and by Winkler t i t r a t i o n . The s o l i d l i n e represents Tone to one correspondence. 21 Model 1131 - the technique used was t o t r a n s f e r the probe from one s o l u t i o n to another. They a l s o do not s t a t e whether or not the f l u i d was kept i n motion to e l i m i n a t e the e x t e r n a l boundary l a y e r e f f e c t . Probably the time-constant i s l e s s than 8 seconds and can be estimated by comparing oxygen s p e c t r a with s p e c t r a of sensors with known time c o n s t a n t s . The i n t e r n a l d i f f u s i o n time remains however so one cannot expect improvement of more than a f a c t o r of two or so. From the s p e c t r a shown l a t e r i t appears the time c o n s t a n t may be 3-5 seconds although the r e s u l t i s not c l e a r cut. 2.5 C h l o r o p h y l l I t was decided to measure c h l o r o p h y l l a ( c h l a) as an index of the standing stock of phytoplankton. T h i s r e p r e s e n t a t i o n i s i n common use with good reason. For example P i a t t and Subba Rao (1970) a r r i v e d at a p a r t i a l c o r r e l a t i o n c o e f f i c i e n t f o r c h l o r o p h y l l a and c e l l number of value 0.81, s i g n i f i c a n t at the 1% l e v e l . The c o e f f i c i e n t f o r c h l o r o p h y l l a, and t o t a l carbon was 0.61, a l s o s i g n i f i c a n t at the 1% l e v e l . Fluorometry i s a method of d e t e r m i n a t i o n of c h l o r o p h y l l a ( f e n t s c h and Menzel, 1963) and was chosen f o r t h i s experiment because i t a l l o w s continuous sampling (Lorenzen, 1966; P i a t t , 1972). A Turner model 111 fluorometer was chosen l a r g e l y because of p r e v i o u s use i n s i m i l a r experiments but a l s o because of the i n i t i a l c o s t , which i s not as s i g n i f i c a n t as f o r other f l u o r o m e t e r s . I t was equipped with a red s e n s i t i v e p h o t o m u l t i p l i e r and a high-volume continuous sampling door. The 22 f i l t e r f o r the e x c i t a t i o n lamp was a Corning CS5-60 and number CS2-64 f o r the emitted l i g h t , f o l l o w i n g S t r i c k l a n d and Parsons (1972). The lamp used was the g e n e r a l purpose u l t r a v i o l e t (c».D. F4T4/BL) because the c o n c e n t r a t i o n s of c h l o r o p h y l l a v a i l a b l e f o r e x c i t a t i o n i n the l o c a l waters are high and use of a more s e n s i t i v e bulb i s not r e q u i r e d . There are problems with the g e n e r a l purpose lamp however i n th a t the warm-up pe r i o d i s e x c e p t i o n a l l y l e n g t h y (Krauel, 1972) . I n i t i a l use of the fluorometer d u r i n g t h i s experiment occurred on average 30 minutes a f t e r being turned on. T h i s i s longer than that rtrrComitt<=nded by the manufacturer but ac c o r d i n g to Krauel i s not long enough to assure c o n s i s t e n c y . However most of the data were taken a f t e r a s u f f i c i e n t l y long p e r i o d that the e r r o r i s n e g l i g i b l e . P r e c a u t i o n s concerning the use of opague hose were di s c u s s e d i n the s e c t i o n on the pumping system. No bubble t r a p s were used s i n c e any bubbles present did not appear t o cause problems. There d i d not seem t o be many forntad i n the f l u i d nor might one expect very many s i n c e the change i n pressure was not great nor was the change i n temperature. No doubt there was soma s c a t t e r i n g of l i g h t by the bubbles that d i d form but i t has been demonstrated that t h i s does not have a great e f f e c t ( K rauel, 1972). The fluorometer was operated with a 1 K£l r e s i s t o r connected from the upper (0-2 MA) post to ground and the span a d j u s t e d so that as the d i a l went from 0-100 the v o l t a g e output would go from 0-1 v o l t . I t was t h i s v o l t a g e that was recorded. For a complete d e s c r i p t i o n of the p r i n c i p l e of the Turner / / I 23 model 111 f l u o r o m e t e r , one i s r e f e r r e d to the manual of o p e r a t i o n and s e r v i c i n g f o r the instrument, but e s s e n t i a l l y i t i s as f o l l o w i n g . The p h o t o m u l t i p l i e r i s surrounded by a mechanically d r i v e n l i g h t i n t e r r u p t e r and sees l i g h t a l t e r n a t e l y from the sample and from a c a l i b r a t e d s o urce. The d i f f e r e n c e between these two s i g n a l s i s a m p l i f i e d and has e i t h e r p o s i t i v e or negative phase depending upon which l i g h t path c o n t a i n s an excess. T h i s output i s detected and used to d r i v e a s e r v o -system. T h i s servo-system w i l l operate u n t i l the amount of l i g h t a r r i v i n g at the p h o t o m u l t i p l i e r i s egual i n both l i g h t paths. The d i a l r e a d i n g or v o l t a g e output i s then r e p r e s e n t a t i v e of the amount of f l u o r e s c e n c e . Because a d i f f e r e n c e s i g n a l i s used, the o p e r a t i n g v o l t a g e may f l u c t u a t e without a f f e c t i n g the measurement and the instrument i s t h e r e f o r e s u i t a b l e f o r o p e r a t i n g on board a s h i p , even without a s t a b i l i z e d pcwer source. C a l i b r a t i o n of the instrument was performed i n the l a b o r a t o r y using c u l t u r e d c e l l s . Attempts at using e x t r a c t e d pigment i n an acetone s o l u t i o n f a i l e d because of high background f l u o r e s c e n c e . T h i s problem occurred even with s p e c t r a l grade acetone. I n i t i a l l y the cause was thought to be the l e a c h i n g of f l u o r e s c e n t substances from the rubber s e a l s used i n the instrument but c o v e r i n g these with p a r a f i l m d i d not a l l e v i a t e the problem and f i n a l l y another approach was used. S o l u t i o n s of the c u l t u r e d c e l l s , a l l pure s t r a i n s , were a p p r o p r i a t e l y d i l u t e d with d i s t i l l e d water to achieve approximately 8-10 readings over the f l u o r e s c e n c e range 0-100. These p o i n t s were then l e a s t - s q u a r e s f i t t e d so t h a t a l i n e a r 24 r e l a t i o n s h i p between f l u o r e s c e n c e and v o l t a g e could be obtained. The d i s t i l l e d water used d i d not measurably f l u o r e s c e and the blank was obtained by c o v e r i n g up the e x c i t a t i o n p o r t . During t r i a l s at sea, t h i s method of b l a n k i n g was shown t o g i v e the same r e s u l t as f i l t e r e d sea-water. The s o l u t i o n of c e l l s was w e l l a g i t a t e d as t o approach homogeneity and the f l u o r e s c e n c e reading was taken almost immediately so t h a t there was l i t t l e chance of the c e l l s s e t t l i n g out of suspension. T h i s method gave r e p r o d u c i b l e r e s u l t s . To o b t a i n the c h l o r o p h y l l a,-voltage r e l a t i o n s h i p , a 500 ml sample of the s o l u t i o n was f i l t e r e d and the pigment content obtained s p e c t r o p h o t o m e t r i c a l l y f o l l o w i n g the method o u t l i n e d i n S t r i c k l a n d and Parsons (19.72). During c a l i b r a t i o n , mathematical r e l a t i o n s between ap e r t u r e s e t t i n g and f l u o r e s c e n t l e v e l were obtained f o r those s e t t i n g s used i n the experiments. The graphs ( f i g u r e 3) of c h l o r o p h y l l versus v o l t a g e are very i n t e r e s t i n g i n t h a t the r e l a t i o n i s d i f f e r e n t f o r each s p e c i e s chosen. T h i s r e s u l t i s confirmed by the work of L o f t u s , Subba Rao and S e l i g e r (1972). Part of t h i s d i f f e r e n c e might p o s s i b l y r e s u l t from d i f f e r e n t p h y s i o l o g i c a l c h a r a c t e r i s t i c s of the s p e c i e s or d i f f e r e n c e s i n e x t r a c t a b i l i t y of the c h l o r o p h y l l . The s p e c i e s chosen f o r c a l i b r a t i o n are a l l common to the l o c a l waters and s i n c e there are d i f f e r e n t c a l i b r a t i o n c o n s t a n t s i n v o l v e d , i n t e r p r e t a t i o n of the p a t c h i n e s s becomes more d i f f i c u l t i f the s p e c i e s e x i s t i n aggregations as c o u l d p o s s i b l y occur. Because Skeletonema Costatum i s the dominant s p e c i e s during the s p r i n g and e a r l y summer (Parsons et a l , 1970) the c o e f f i c i e n t s from i t s c a l i b r a t i o n were used. 25 SO 40 10 E E 30 J 20 4 X u 10 • < K E L E T O N E M A C O S T A T U M • 0 L I S T M 0 D I S C U 8 L U T S U S O P S E U O O P E D I N E L L A P Y R I F 0 R M I 3 A C R Y P T O M A S P R O F U N D A — 0 1.0 V O L T S f i g . 3; Calibration curves for the fluorometer for different species common to local British Columbia waters. The curve for Skeletonema was chosen for fi n a l calibration because of i t s dominance of the phyto-plankton f i e l d in Georgia Strait during the sampling period 26 According t o the manufacturer, the f l u o r o m e t e r w i l l respond such that 90% of a step change i s accomplished i n 5 seconds. Thus the time c o n s t a n t which i s the time f o r a 63% change i s about 2-3 seconds and the s p e c t r a l l e v e l i s 1/2 the t r u e value a t a frequency of about 0.06 Hz or a length s c a l e of about 15 meters. 2.6 V e l o c i t y F l u c t u a t i o n s I n i t i a l l y the experiment i n c l u d e d measurement of v e l o c i t y f l u c t u a t i o n s . The i n s t r u m e n t a t i o n i n v o l v e d a Disa anemometer with the sensor being a Disa 55R32 wedge shaped probe. T h i s probe was developed f o r use i n conducting f l u i d s . U n f o r t u n a t e l y there were problems with the use of these sensors and two were s e r i o u s l y damaged so as to be i n o p e r a t i v e . The s i g n a l s o f t e n c o n t a i n e d d i s r u p t i o n s and d i s p l a y e d " s p i k e s . " These are thought to be the r e s u l t of plankton-probe c o l l i s i o n s . No c a l i b r a t i o n s were done but the r e s u l t s of some good data are i n c l u d e d i n an appendix with the hope that something of the nature of the f l u c t u a t i o n s might be i n f e r r e d from the s p e c t r a l shapes and coherency. 2.7 Mean V e l o c i t y The mean r e l a t i v e ship-water v e l o c i t y was measured with a General Oceanics model 2031 d i g i t a l flowmeter and model 2035 flowmeter readout. The manufacturers s p e c i f i c a t i o n s g i v e the t h r e s h o l d v e l o c i t y as 17 cm/sec and the l i n e a r range as being 27 between 26 cm/sec and 5.1 m/sec. The flowmeter i s a p r o p e l l o r device whch c o n t a i n s an e l e c t r o n i c c i r c u i t w i t h i n . R o t a t i o n of the p r o p e l l o r causes c l o s u r e of a reed s w i t c h , and a p u l s e i s sent to the onboard readout where a c a p a c i t o r i s charged. The charge of the c a p a c i t o r i s p r o p o r t i o n a l to the number of p u l s e s and t h e r e f o r e t o t h e v e l o c i t y . T h i s v o l t a g e i s used t o d e f l e c t the needle of a meter f o r the v i s u a l d i s p l a y of speed and f o r the measured s i g n a l . C a l i b r a t i o n of the flowmeter was completed i n two stages. F i r s t l y , a r e l a t i o n between v o l t a g e and meter readi n g was determined by mechanically s p i n n i n g the p r o p e l l o r , measuring the vo l t a g e and noting the needle d e f l e c t i o n . Then the flowmeter was placed i n a flume tank at the C i v i l e n g i n e e r i n g h y d r a u l i c s l a b o r a t o r y at U.B.C. and the readout was compared t o t h a t of an already c a l i b r a t e d flowmeter. A c a l i b r a t i o n e g uation i n v o l v i n g v o l t a g e and v e l o c i t y was the r e s u l t cf removing the common measurement from the two r e l a t i o n s h i p s . The data p o i n t s were f i t t e d l i n e a r l y with the e r r o r i n the s l o p e e v a l u a t i o n being approximately 3%. 2.8 S i g n a l P r o c e s s i n g F i g u r e 4 i s a schematic of the s i g n a l pathway, the f i n a l stage being d i g i t i z a t i o n and sto r a g e on magnetic computer tape. The output v o l t a g e s of three of the instruments (the sal i n o m e t e r , the oxygen meter, and the flowmeter) are s m a l l and to ensure a good s i g n a l to r e c o r d , p r e a m p l i f i e r s designed by 0 X Y 6 E N S A L I N I T Y u x H < d F L O W M E T E R T E M P - I N BRIDCf T E M P . O U T F L U O R 0 -M E T E R W E 9 6 C IO«E> [ANEMO METER b l u . o < » o * > . B R U S H R E C O R O E R O I S C R I M I N A T O R F I L T E R S A - 0 C O N V E R T E R S I G N A L P R O C E S S I N G i g . 4: A schematic o f the s i g n a l pathway from instrument t o computer. 29 Mr. E. Meyer were used. These a m p l i f i e r s a l s o f i l t e r e d the th r e e s i g n a l s to remove noise present a t the higher f r e g u e n c i e s . F l o a t i n g i n p u t s i s o l a t e d the instruments from ground. I n i t i a l e l e c t r o n i c problems were ground l o o p s , probably caused by the d i f f e r e n c e i n p o t e n t i a l between the s h i p ' s h u l l and sea water. To e l i m i n a t e the l o o p s , i t was necessary t o i s o l a t e the instruments from the h u l l a l t o g e t h e r . The h o t - f i l m probe uses sea-water as i t s r e f e r e n c e and a l l i n s t r u m e n t a t i o n was grounded through i t . A Hewlett-Packard i n s t r u m e n t a t i o n tape r e c o r d e r with Scotch 290 tape recorded the data. Because of dynamic range l i m i t a t i o n s and to maximize the s i g n a l t o noise r a t i o of the f l u c t u a t i o n s i n the s i g n a l s , some d.c. v o l t a g e was removed before r e c o r d i n g . T h i s d.c. v o l t a g e i s r e f e r r e d t o as o f f s e t . F u r t h e r a m p l i f i c a t i o n a t t h i s stage c r e a t e d optimum r e c o r d i n g c o n d i t i o n s . Before being placed on tape however, the s i g n a l s were frequency modulated and m u l t i p l e x e d . During data a c q u i s i t i o n , t he recorded s i g n a l was si m u l t a n e o u s l y demodulated and d i s p l a y e d on c h a r t paper so t h a t the data c o u l d be monitored. S e l e c t e d p i e c e s of the data were d i g i t i z e d using the I n s t i t u t e ' s P.D.P.-12 computer and pl a c e d on IBM compatible tape f o r a n a l y s i s u s i n g the model 370 computer a v a i l a b l e at U.B.C. Before d i g i t i z a t i o n each s i g n a l was passed through simple EC f i l t e r s with a corner frequency of approximately 1 Hz. Thus a r e l a t i v e l y slow sampling r a t e of 4 Hz c o u l d be used without f e a r of a l i a s i n g back n o i s e at higher f r e q u e n c i e s . B a r t l e t t ' s procedure (Bendat and P i e r s o l , 1971) of smoothinq was u t i l i z e d as the d i g i t i z e d s i g n a l was d i v i d e d i n t o 30 blocks of 1024 d i g i t i z e d p o i n t s f o r t r a n s f o r m a t i o n so t h a t 1024 c o e f f i c i e n t s were recovered. Band averaging was a l s o done, but i n a manner such t h a t when the s p e c t r a l e s t i m a t e s are p l o t t e d a g a i n s t l o g f , they appear to be e q u a l l y spaced with about 8 po i n t s per decade. Thus as frequency i n c r e a s e s , the averaging i s done over more harmonics. 31 CHAPTER I I I ANALYSIS TECHNIQUE 3.1 I n t r o d u c t i o n In t h i s c h a p t e r , an attempt i s made to f a m i l i a r i z e the reader with the fundamentals of a n a l y s i s used to e x t r a c t i n f o r m a t i o n from the o r i g i n a l data. I f we have time s e r i e s r e c o r d s of some parameters, how do we g a i n knowledge of these v a r i a b l e s and t h e i r r e l a t e d n e s s with others? S e l e c t e d data segments are co n s i d e r e d to be samples of a s t o c h a s t i c process and s t a t i s t i c a l q u a n t i t i e s such as v a r i a n c e , c o v a r i a n c e and s p e c t r a are computed using a p p r o p r i a t e sums and products of t h e i r F o u r i e r c o e f f i c i e n t s which are c a l c u l a t e d from the data and can be used as a r e p r e s e n t a t i o n of them. Time s e r i e s a n a l y s i s and the treatment of random data are the s u b j e c t s of e n t i r e books and f o r a complete d e s c r i p t i o n one i s d i r e c t e d to J e n k i n s and Watts (1968) and Bendat and P i e r s o l (1971). The a c t u a l computer programs used are d e s c r i b e d i n G a r r e t t (1970). 3. 2 F o u r i e r Transformation Suppose t h e r e i s a time v a r y i n g process X(t) from which a sample of d u r a t i o n T i s taken, c a l l i t s ( t ) . T h i s sample need not be p e r i o d i c but i t can be approximated using p e r i o d i c 32 f u n c t i o n s . F o u r i e r a n a l y s i s uses s i n e and co s i n e f u n c t i o n s . T h e r e f o r e the data s <t) can be represented by the f i n i t e F o u r i e r s e r i e s u s(t) = £ ( A m cos2TTmft + Bmsin2TTmft) 3.2.1 Here m i s an i n t e g e r q u a n t i t y and we l e t f9 - 1/T be the fundamental frequency, e n s u r i n g o r t h o g o n a l i t y of the s i n e s and c o s i n e s . In order to use the Fa s t F o u r i e r Transform (FFT) technique t o o b t a i n the c o e f f i c i e n t s , the analog s i g n a l s (t) i s d i g i t i z e d or sampled at e q u a l l y spaced i n t e r v a l s i n t i m e , A , t o o b t a i n a d i s c r e t e s i g n a l S r c o n t a i n i n g r = T/A samples. In our case the number c f samples was a power of 2, although other bases may be used, and wa can w r i t e T/A = N = 2L 3.2.2 Replacing t by r A and f by 1/N we can write s, = £(A-cos2TTmr + Bmsin2TTmr) r = 1, N 3-2-3 and o r t h o g o n a l i t y r e l a t i o n s are "Z. sin2TTkr cos2TTmr =0 k. m inte g e r s %, sin2TTkr sin2Jfmr =0 k i m = L k = m / 0, L = 0 k = m = 0, L 3.2.4 3.2.5 33 cos2TT_kr cos2Tfmr = 0 k 4 m r* 1 N N = L k = ra ^  0, L = N k = m = 0, L 3.2.6 Multiplying both sides of 3.2.3 by either cosZTJjnr or N sinZTTmr and summing over r gives the c o e f f i c i e n t s N H Am = s r cos2TTmr 3.2.7 N r e l . N B W 1 = 1 ^ s r sin2TTmr 3.2.8 N r t i N These e x p r e s s i o n s f o r the c o e f f i c i e n t s are s a t i s f i e d i f S f takes the form s P = A 0 + £ (A wcos2TTmr + B msin2TTmr) + A v cosTfr 3.2.9 2 W» ; N " I T - 2 r = I, N T h i s equation r e a l l y r e p r e s e n t s a s e t of N equations which can be s o l v e d f o r N c o e f f i c i e n t s . So now we have N F o u r i e r c o e f f i c i e n t s r e s u l t i n g from N d i g i t i z e d p o i n t s . The zero frequency component A e/2 r e p r e s e n t s the a r i t h m e t i c mean or i n e l e c t r i c a l terms, t h e d.c. l e v e l of the s i g n a l . The i n f o r m a t i o n i n frequency space i s band l i m i t e d , t h a t i s the i n f o r m a t i o n i s c o n t a i n e d between the lowest frequency present and the h i q h e s t . E x c l u d i n q zero frequency, the lowest frequency i s 1/NA , the fundamental, which corresponds to a p e r i o d equal t o the r e c o r d l e n g t h T. The h i g h e s t frequency, sometimes c a l l e d the Nyquist frequency i s 1 / ( 2 A ) which corresponds t o a p e r i o d of 2 sampling i n t e r v a l s . Information o u t s i d e o f t h i s band i s not e x t r a c t e d 3a u s i n g t h i s method. I f the sampling i n t e r v a l , A , i s too l a r g e so t h a t some high frequency components are not i n c l u d e d i n the band, then a l i a s i n g can occur. T h i s means t h a t i n f o r m a t i o n t h a t i s con t a i n e d at these unresolved high f r e q u e n c i e s w i l l appear a s s o c i a t e d with one of the f r e q u e n c i e s c o n t a i n e d w i t h i n the r e s o l v e d band. T h i s " f o l d i n g " as i t i s sometimes c a l l e d a c t s l i k e a m i r r o r p o s i t i o n e d a t the Nyquist frequency so t h a t i n f o r m a t i o n c o n t a i n e d at 1 / ( 2 A ) + f w i l l appear a t 1 / ( 2 A ) - f . To prevent t h i s problem, the analog data were f i r s t f i l t e r e d before d i g i t i z a t i o n t o remove energy at higher f r e q u e n c i e s . 3.3 Sp e c t r a and Coherence P a r s e v a l ' s theorem g i v e s us t h e average power or mean square value of S^, 1 £ 3.3.1 N r n Using the o r t h o g o n a l i t y r e l a t i o n s t h i s becomes l £ s r = l f e j n _ L B L ) + A . c + 3.8.2 N rsi m:\ 2. 4 4 More o f t e n we are i n t e r e s t e d i n the power about the mean r a t h e r than about zero. T h i s i s the v a r i a n c e or i n e l e c t r i c a l language, the average a.c. power. a = l £ ( s r - A 0 ) 1 N r s» 2 = £ (Am + ) + 3.3.3 >n«i 35 I f we p l o t the power f o r each harmonic a g a i n s t the freguency of t h a t harmonic we have a F o u r i e r l i n e spectrum, but i t i s more us u a l t o t r e a t the power as a conti n u o u s f u n c t i o n of freguency. To do t h i s we d e f i n e a power s p e c t r a l d e n s i t y f u n c t i o n " J ( f ) such t h a t the i n t e g r a l o f t h i s f u n c t i o n over a l l f r e g u e n c i e s g i v e s the t o t a l v a r i a n c e C% = ) $ ( f ) d f 3.3.4 c or i n d i s c r e t e terms where At corresponds to 1 / ( H A ) and "§;B r e p r e s e n t s the c o n t r i b u t i o n t o t h e va r i a n c e of the b a n d ( f m - A f / 2 ) t o ( f ^ * A f / 2 ) N 3.3.5 f*\ . 3.3.6 we are a l s o i n t e r e s t e d i n a measure of the r e l a t e d n e s s o f two time s e r i e s . Suppose we have two simultaneous s i g n a l s whose d i s c r e t e F o u r i e r r e p r e s e n t a t i o n s a r e : s t r = Ajp + £ (Amcos2jTTmr + B sin2TTmr) + Atwcos2TfLr 3.3.7 2 m« i N N 2 N \r = Azo + i (A2ncos2TTmr + B?nsin2TTmr) + AZLcos2TTLr . 3.3.8 2 mc| N N 2 N r = 1, N . For b r e v i t y , t he s i g n a l s w i l l be assumed to have ze r o means so t h a t A , 0/2 = A X o /2~ 0. We can w r i t e one averaged product c a l l e d the c o - v a r i a n c e as 1 £ s t < r s,,. =•£ (hxm A g ^ t B , m B t f t t ) + A l k . 3.3.9 N r«i m s , 2 4 However, t h i s product assumes the s i g n a l s a r e i n phase with one another and t h i s i s not n e c e s s a r i l y t r u e . we can a l s o form another product by s h i f t i n g the phase of one s i g n a l by 90 at each frequency denoted by s ^ . The averaged product c a l l e d the quad-variance Is N JJL V-t It s . r \r = £ A ^ B i m - A » W Hm . 3.3.10 N T s | 0 ! e , 2 These c o n t r i b u t i o n s to the v a r i a n c e can a l s o be w r i t t e n as s p e c t r a l d e n s i t y f u n c t i o n s which f o r a s i n g l e frequency are Co = A > m A ^ m + B t w > B X N 3.3.11 . 2 A f £ « m = A 2 w t B l w - A i m B l h t 3.3.12 2 A f A A Co t ^ (f) i s c a l l e d the C o i n c i d e n t or Co-spectrum and Qn{1_ (f) i s the Quadrature or Quad-spectrum. The cross-spectrum may be thought of as a v e c t o r i n the complex plane with components A A Co%x(f) and Qu l v(f) being the r e a l (in-phase) and imaginary (TT/2 out of phase) p a r t s r e s p e c t i v e l y , A A A = C oVl/ f) - 3 Q u | X ( f ) 3.3.13 where j =/-1*. The l e n g t h or magnitude o f t h i s v e c t o r i s g i v e n by: J & = I C o ^ ( f ) + Q u ^ ( f ) J 3.3.14 and the angle from the r e a l a x i s by © ( f ) = t a n ' ^ - Q u t x ( f ) ^ ^ 3.3.15 37 Now i f the two s i g n a l s were i n phase t o t a l l y , t here would be zero c o n t r i b u t i o n from Quadrature and i f they were 90 out of A phase, the Co-spectrum would be zero, so t h a t we see © i s the phase angle between the two s i g n a l s . There i s another s t a t i s t i c we can form to t e s t the r e l a t e d n e s s of these two s i g n a l s , the squared coherence f u n c t i o n , d e f i n e d as 3.3.16 An a r t i f a c t of the a n a l y s i s i s that t h i s f u n c t i o n equals 1 a t each i n d i v i d u a l freguency k/T. T h i s can be demonstrated by e v a l u a t i n g the sguared coherence at harmonic k which i s x. i -= (A t t f A,.,t + B t l t B y ) + (B .K, A t w - A I K B 1 K ) = 1 . 3.3.17 E s s e n t i a l l y coherence measures how well a s t r a i g h t l i n e approximates the data p o i n t s (Bendat and P i e r s o l , 1971). At one harmonic and with no averaging, the coherence estimate has 2 degrees of freedom, analagous to drawing a s t r a i g h t l i n e between 2 data p o i n t s which of course can always be done. The r e f o r e f o r any coherence e s t i m a t e based on 2 degrees of freedom, the r e s u l t w i l l always be 1. However i f the s p e c t r a l e s t i m a t e s are s u i t a b l y smoothed by averaging before coherence i s c a l c u l a t e d , 2^ takes on values between 0 and 1; 0 i f the two s i g n a l s are s t a t i s t i c a l l y u n r e l a t e d and 1 i f they are p e r f e c t l y r e l a t e d . Thus smoothing g i v e s us a r e s u l t which i s r e l a t e d to the data 38 r a t h e r than to the a n a l y s i s technique. 3.4 Smoothing - Windowing The p r e v i o u s s e c t i o n s demonstrated the c o n s t r u c t i o n of power s p e c t r a and c r o s s - s p e c t r a from F o u r i e r c o e f f i c i e n t s . U n f o r t u n a t e l y these e s t i m a t e s are i n e r r o r because they are based on knowledge of a f i n i t e d u r a t i o n o f data, t h a t i s they are each only one sample of a l a r g e p o p u l a t i o n . A sample can be considered to be the product of an i n f i n i t e time s e r i e s and a f u n c t i o n t h a t equals u n i t y f o r the d u r a t i o n of the sample and zer o everywhere e l s e . T h i s f u n c t i o n i s o f t e n r e f e r r e d t o as a boxcar f u n c t i o n . Althouqh the product i n time g i v e s us an exact r e p r e s e n t a t i o n of the i n f i n i t e s i g n a l w i t h i n the sampling p e r i o d , the r e p r e s e n t a t i o n o f the product i n freguency space i s more complicated and i n v o l v e s a c o n v o l u t i o n . For example, suppose we have an x(t) with t r a n s f o r m X (f) and another f u n c t i o n w(t) with transform W ( f ) , then the transform of the product i s given by s ( f ) = |x(jf')w(f - f # ) d f 3.4.1 w now i f we l e t w(t) be the boxcar f u n c t i o n ?(t) =1 0 i t i T = 0 t * 0 ; t > T 3.4.2 T H E N / T . :WTH W(f) = V e dt "3 ( 1 - g__ J 3.4.3 39 and the c o n v o l u t i o n becomes S ( f ) = J X ( ^ ) - e n _ 3 . 4 . 4 where the f u n c t i o n -V) / - 3 ^1 J 3 . 4 . 5 i s c a l l e d the s p e c t r a l window. The e f f e c t of the s p e c t r a l window can be demonstrated i n an example which f o l l o w s that of G a r r e t t (1970) . Suppose we have a s i g n a l which c o n s i s t s e n t i r e l y o f the s i n u s o i d v ^e"* h > °^ , where td0 = 2TTf 0 and ^ i s complex, which f o r convenience can be w r i t t e n as x ^ e = (A - 3 B)e « 3 . 4 . 6 I f we sample f o r a p e r i o d T, the r e s u l t i n g transform w i l l be dt o 3"(A - jB) ) = R+ j i 3 . 4 . 7 where R = Asin((o c-tQ )T + B ( l - cos(Qe-ti> )T) 3 . 4 . 8 I = A ( l - cos(t3 0-U> )T) - Bsim'( tD 0-U))T . 3 . 4 . 9 io 0 - u> The spectrum i s 40 = CA 3.4.11 3.4.12 N o w i f to = (*>e then t h i s reduces t o 1 C ^  + I* ) = ( A X + B V )T = A V + 2T 2 2Af but i f W ^ c0 o then the e f f e c t i s t o " l e a k " v a r i a n c e t o other f r e q u e n c i e s as allowed by the f u n c t i o n 1 - cos( top-10' )T . 3.4.13 ( » 0 - W ) T In the case of a d i s c r e t e l y sampled s i g n a l we need f o r e p l a c e T with NAt and u» with 2TTk/NAt where k i s an i n t e g e r l e s s than (N/2)H. Any energy i n the o r i g i n a l s i g n a l which i s a t a frequency t h a t i s n ' t an i n t e g e r m u l t i p l e o f (N^t) w i l l leak to neighbouring bands. T h i s can be a s e r i o u s problem i f there are l a r g e peaks i n the spectrum or i f the low f r e q u e n c i e s c o n t a i n a grea t d e a l more energy than the higher f r e g u e n c i e s s i n c e the leakage w i l l mask the s m a l l e r c o n t r i b u t i o n s from the high f r e q u e n c i e s and the spectrum w i l l have an i n c o r r e c t shape i n t h i s r e g i o n . T h e r e f o r e , to o f f s e t problems l i k e t h e s e , i t i s necessary t o smooth or a l t e r the shape of the window. One method of a l t e r i n g the shape of the window, i s to d i v i d e the o r i g i n a l sample i n t o segments of s h o r t e r d u r a t i o n . I f the o r i g i n a l sample was o r i g i n a l l y T i n l e n g t h , we d i v i d e i t i n t o segments o f l e n g t h T/p and tran s f o r m each segment i n d i v i d u a l l y , averaging the r e s u l t s t o o b t a i n the estimate. 4 1 T h i s reduces the leakage but a l s o l i m i t s the r e s o l u t i o n of the procedure s i n c e the bandwidth i s new p/T i n s t e a d of 1/T as be f o r e . T h i s window i s the B a r t l e t t window and a more complete d e s c r i p t i o n i s given i n Je n k i n s and watts (1968). Another way to a l t e r the s p e c t r a l window i s to average together the r e s u l t s of r neighbouring harmonics. T h i s i s d e s c r i b e d i n Bendat and P i e r s o l (1971). These averaging technigues a l s o reduce the standard e r r o r of the s t a t i s t i c a l q u a n t i t i e s i n v o l v e d . As d e s c r i b e d above, the F o u r i e r c o e f f i c i e n t s are the s o l u t i o n to a s e t of N independent equations r e l a t i n g N c o e f f i c i e n t s to N/2 f r e q u e n c i e s . These c o e f f i c i e n t s , at each harmonic can be con s i d e r e d to be u n c o r r e l a t e d random v a r i a b l e s (Bendatt and P i e r s o l , 1 9 7 1 ) . I f the o r i g i n a l sample i s Gaussian, then these c o e f f i c i e n t s w i l l be Gaussian as w a l l , and a s i n g l e s p e c t r a l estimate w i l l be d i s t r i b u t e d as )£ 2 with 2 degrees of freedom. The s p e c t r a l estimate at frequency f w i l l have the d i s t r i b u t i o n •L S ( f , T) = Xx 3 . 4 . 1 4 and the normalized standard e r r o r w i l l be £ f =JT 3 . 4 . 1 5 where n i s the number of degrees of freedom which i n t h i s case i s 2 given a 100% normalized standard e r r o r . The e f f e c t of the B a r t l e t t window i s to reduce t h i s by a f a c t o r of ]f^/f a n d averaging over s u c c e s s i v e r harmonics f u r t h e r reduces t h i s by ^ \/r so t h a t the two together reduce the standard e r r o r to 42 £ r 5 J^p* The s t a t i s t i c s of the averaging procedure are d i s c u s s e d i n Bendatt and P i e r s o l (1971). 3.5 S t a t i s t i c a l Accuracy We are a l s o i n t e r e s t e d i n the s t a t i s t i c a l accuracy of our e s t i m a t e s , or how c l o s e our sample e s t i m a t e s are to a " t r u e " value t h a t would be o b t a i n e d with an i n f i n i t e r e c o r d . T h i s i s e s p e c i a l l y t r u e f o r the values of coherence s i n c e they are an Important measure o f s i m i l a r i t y . In the coherence e s t i m a t e s , we have numbers which e s s e n t i a l l y t e l l us how w e l l two s i g n a l s are r e l a t e d , and we would l i k e t o know how these compare t o " t r u e " values as w e l l as t h e i r s i g n i f i c a n c e . One might t h i n k there i s an element of redundancy i n t h i s l a s t statement, but i t might be more understandable i f I t were put another way. For each coherence estimate we would l i k e to have a c o n f i d e n c e r e g i o n i n which the t r u e value of coherence most l i k e l y l i e s o r a t l e a s t has a high p r o b a b i l i t y of doing so. In a d d i t i o n we would a l s o l i k e to know a l e v e l of coherence, above which there would be l i t t l e p o s s i b i l i t y of having a coherence v a l u e obtained from two t o t a l l y u n c o r r e l a t e d s i g n a l s . T h i s s i g n i f i c a n c e l e v e l r e s u l t s from t e s t i n g the n u l l h y p othesis. E m p i r i c a l s t u d i e s (Bendat and Piersol,1971) have shown t h a t i n c e r t a i n i n s t a n c e s , 0.35£ ^f^^O ^ 0.95, n 5- 20 degrees of freedom, a c o n f i d e n c e i n t e r v a l can be c o n s t r u c t e d u s i n g a t r a n s f o r m a t i o n 43 w(f) = 1 ln( 1 + faf)) = tanh' XTf) 3.5.1 where w (f) has an approximately normal d i s t r i b u t i o n . The (1 -A) c o n f i d e n c e band i s given by tanh(w(f) - (n - 2)'- (n - 2) z ^ < %(f) * tanh(w(f). - (n - 2)"*+ (n - i f z ^ 3.5.2 The number of degrees of freedom i n the band over which the estimate was made i s n ( which eguals bandwidth x (2/TTf) or the t o t a l number of F o u r i e r c o e f f i c i e n t s (sine and cosine) i n the band) and z ^ i s the 100 percentage p o i n t of a s t a n d a r d i z e d normal d i s t r i b u t i o n . The value of ^ f o r 95% c o n f i d e n c e i s 1.96. As an example suppose we want t o c o n s t r u c t the 95% c o n f i d e n c e band f o r an estimate with 22 degrees of freedom. The value of "u"^  i s 0.5. The corresponding l i m i t s f o r the i n t e r v a l are 0. 38 <• 0.54. Eguation 3.5.1 g i v e s us a r e g i o n i n which the t r u e value of coherence w i l l l i e as a f u n c t i o n of I t i s a l s o p o s s i b l e to o b t a i n a c o n f i d e n c e i n t e r v a l f o r the phase s p e c t r a l e s t i m a t e s and the procedure i s o u t l i n e d i n J e n k i n s and Watts (1968). The 95% c o n f i d e n c e i n t e r v a l f o r the tangent of the phase esti m a t o r i s determined by e v a l u a t i n g the e x p r e s s i o n 1.96 fsec4© 1 ( 1-1) . 3.5.3 n ll The method used to determine s i g n i f i c a n c e l e v e l s i s e x p l a i n e d i n Groves and Hannan (1968). I t i n v o l v e s an assumed d i s t r i b u t i o n of p r o b a b i l i t y d e n s i t y f o r p a r t i a l coherence which i s a f u n c t i o n of t r u e coherence, degrees of freedom and sample coherence. He t e s t the n u l l h y p o t h e s i s , t h a t i s the case of 0 true coherence using the equation Fp tffyo) = 1 - (1 _o'tj )) where Fp Ofyo) i s the l e v e l of s i q n i f i c a n c e , and i s the coherence squared value below which any random coherence (true value zero) w i l l f a l l with c e r t a i n t y F p ( ^ ^ O ) and M i s the number of degrees of freedom d i v i d e d by 2. Osinq n=22 and Fp(H,/0) = 0.95 we f i n d T£^= 0. 259 or ^ = 0. 509. The c o n f i d e n c e bands f o r the s p e c t r a l e s t i m a t e s t h a t w i l l be presented are net based on an assumption i n v o l v i n q t h e i r expected d i s t r i b u t i o n , but r a t h e r on the v a r i a b i l i t y i n the estimates between blocks as d i s c u s s e d i n the next c h a p t e r . 3.6 Treatment of the Data To r e i t e r a t e s e c t i o n 2.8, t h e analogue s i g n a l was d i g i t i z e d with a sampling freguency of 4 Hz. and d i v i d e d i n t o s e c t i o n s of 1024 p o i n t s c a l l e d b l o c k s , to be F o u r i e r transformed. S p e c t r a l a n a l y s i s was done on s e v e r a l s e g u e n t i a l b l o c k s of the transformed data using the SCOR programs of G a r r e t t (1970). The range of p e r i o d s t h a t c o u l d be i n v e s t i g a t e d using t h i s method i s between 256 sees and 0.5 sees. I t i s expected t h a t t u r b u l e n t f l u c t u a t i o n s i n the speed were much l e s s than the mean of about 1 m/sec so t h a t T a y l o r ' s h y p o t h e s i s , that i s , l e n g t h x freguency = mean speed of flow (Hinze, 1959) can be used to e x t r a p o l a t e to l e n g t h s c a l e s of about 256 m t o 0.5 m. However because of the response l i m i t s of U5 s o i e of the i a s t r u a e n t s which w i l l tend to smooth out s i a a l l s c a l e fluct«ati«ns, the e f f e c t s of the puap and the approach to the system noise l e v e l because of t h e s m a l l s p e c t r a l v a l u e s a t high frequency, the s a a l l e s t s c a l e t h a t can be d i s c u s s e d with c o n f i d e n c e i s probably about 10 a. I t i s p o s s i b l e to examine l a r g e r s c a l e s using the SCOR-low option of the SCOR program. This e x t e n s i o n i s c a r r i e d out by F o u r i e r t r a n s f o r m i n g and s p e c t r a l a n a l y z i n g the b l o c k averages and was done f o r data with between 10 and 19 b l o c k s . Where the number of b l o c k s was not a power of 2, then the SCOK-low r e s u l t s are based on e i t h e r l e s s b l o c k s than the high frequency r e s u l t s , or the number o f block averages f o r t r a n s f o r m a t i o n was added t o , using the mean of the a c t u a l block averages t o complete the data. T h i s was done when the data r e c o r d c o n s i s t e d of l e s s than 16 b l o c k s , f o r example the June Howe Sound 5a data. When p l o t t e d , the SCOR-lcw s p e c t r a l e s t i a a t e s are n o t i c e a b l e as they l a c k confidence bands. The coherence and phase f o r these e s t i a a t e s were not p l o t t e d .since they are 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 , having too few degrees of freedom. The SCOR-low s p e c t r a l r e s u l t s should not be used t o examine d e t a i l s but r a t h e r i n d i c a t e t r e n d s i n the l a r g e s c a l e behaviour of the parameters. By u s i n g a l l the SCOR-low r e s u l t s , a f t e r n o r m a l i z i n g , i t i s p o s s i b l e t o make some e s t i m a t e s of the average coherence f o r a l l the data i n SCOR-low frequency range. D e t a i l s are given, i n the next chapter. 46 CHAPTER IV RESDLTS 4.1 I n t r o d u c t i o n In t h i s c h a p t e r , the r e s u l t s of the a n a l y s i s are presented. F i r s t l y the sampling method i s d i s c u s s e d with i t s e f f e c t s on the r e s u l t s . Then there i s a b r i e f comment on the s t a t i o n a r i t y of the data. I n d i v i d u a l data runs are d i s c u s s e d , i n terms of s p e c t r a and coherence, and f i n a l l y some ••average" r e s u l t s are presented. 4 . 2 The Sampling Method Ship-board i n s t r u m e n t a t i o n n e c e s s i t a t e d the pumping of water from depth through a 30 a l e n g t h of hose. Ther e f o r e i t was t o be expected that the s t r u c t u r e measured a f t e r pumping would be a l t e r e d from t h a t i n s i t u . To g u a n t i f y the d i f f e r e n c e i n some manner, t h e r m i s t o r s were used t o measure temperature before and a f t e r pumping. , In the absence of mixing, and assuming no l o s s or gain of heat d u r i n g t r a n s i t , the s i g n a l s from the two t h e r m i s t o r s should be i d e n t i c a l , as should t h e i r s p e c t r a (apart from s l i g h t d i s s i m i l a r i t i e s because the pump i n t a k e averages over about a 10 cm depth). Therefore some d e s c r i p t i o n of the e f f e c t s of pumping can be obtained by p l o t t i n g the s p e c t r a l r a t i o X ^ ^ / ^ f ^ ( ^  i s 47 e x p l a i n e d on page 35). We expect f l u c t u a t i o n s produced by mixing i n the hose to be o f s c a l e s of order 10 times the diameter of the pipe and these s c a l e s correspond to p e r i o d s s m a l l e r by about a f a c t o r of 5 than the 1/2 power or 3db p o i n t of the analog f i l t e r s used t o prepare the s i g n a l s foe d i g i t i z a t i o n . T herefore the gain f a c t o r ?5.-ren(/5-ro«rJ w i l l only d e s c r i b e the smoothing due to mixing w i t h i n the hose. F i g . 5 c o n t a i n s p l o t s of g a i n f a c t o r s f o r some of the data runs t o be d i s c u s s e d f u r t h e r on. The symbols* d e s i g n a t i o n s are e x p l a i n e d i n t a b l e I. At very l a r g e s c a l e s we would expect a g a i n of 1 and where t h i s doesn't occur, then t h e r e i s a p o s s i b l e c a l i b r a t i o n e r r o r . The shapes are g e n e r a l l y s i m i l a r t o a low pass f i l t e r with a 3db p o i n t a t roughly 10m ( l o g f = -1.0 or f = 0.1 Hz and t h e r e f o r e *\ = 10m.). But i n t e r e s t i n g l y , the g a i n passes through a minimum and then r i s e s to about a value cf 1 i n the very high f r e q u e n c i e s . The q u e s t i o n i s now t o e x p l a i n the shape of the g a i n c u r v e s , a task which i s f a c i l i t a t e d with the a i d of s p e c t r a l p l o t s . For example, the temperature s p e c t r a f o r the June Indian Arm 5 m data are shown i n f i g . 6. The s p e c t r a l e s t i m a t e s have been p l o t t e d a g a i n s t l o g d i s t a n c e i n s t e a d of l o g frequency; the c o n v e r s i o n was done using T a y l o r ' s h y p o t h e s i s as mentioned i n the p r e v i o u s chapter and i s i l l u s t r a t e d l a t e r with equation 4.4.2. The mean speed used f o r the c o n v e r s i o n was the averaqe speed over the data segment chosen f o r a n a l y s i s . The v e r t i c a l bars a s s o c i a t e d with each s p e c t r a l estimate correspond to 68% c o n f i d e n c e i n the mean. They were obtained using the a c t u a l v a r i a b i l i t y i n the i n d i v i d u a l block values (the average of these 1 0 -0-8 a 0-6 o e a o^ 0-2-4 JUNE • 15 — JULY A HI — • GSI O 6 S 3 — A GSS 0*1 " 2 - i o L O G f f i g . 5: P l o t s of the gain f a c t o r s f o r various data runs. These "are r e p r e s e n t a t i v e of the f i l t e r i n g a c t i o n of the pump-hose combination. Symbols are explained on page 60. 00 I 5- JUNE f i g . 6: Temperature s p e c t r a f o r Indian Arm 5m data. Temp i s the t h e r m i s t o r that was on board s h i p , T-out was i n the water. 50 v a l u e s i s the estimate t h a t i s p l o t t e d ) , and assumes a c h i -sguared d i s t r i b u t i o n f o r the square of the modulus of the F o u r i e r c o e f f i c i e n t s . The procedure i s completely e x p l a i n e d i n G a r r e t t (1970). The SCOR-low estimates which were d i s c u s s e d i n the previous chapter have no e r r o r bars a s s o c i a t e d with them s i n c e they are based on F o u r i e r a n a l y s i s of the block averages and do not r e p r e s e n t the means of i n d i v i d u a l b l o c k values. Although a s t a t i s t i c a l e r r o r c o u l d be c o n s t r u c t e d by assuming a d i s t r i b u t i o n f o r the estimates t h i s would be i n c o n s i s t e n t with the p r e s e n t a t i o n of the s m a l l e r s c a l e r e s u l t s and was not done. The e r r o r bars at the l a r g e r s c a l e s of the SCOR a n a l y s i s should a l s o be i n d i c a t i v e of the e r r o r s expected i n the SCOR-low r e s u l t s . The s m a l l h o r i z o n t a l bars of each p l o t are not l i n k e d i n any way with the bandwidth of the e s t i m a t e s but are simply a r t i f a c t s of the p l o t t i n g . The l a r g e r s c a l e s , down to about 20-30 m are s i m i l a r ; at s m a l l e r s c a l e s there appear d i f f e r e n c e s i n the r c l l - o f f c h a r a c t e r i s t i c s probably because of the f i l t e r e f f e c t of the pump and hose system. At about 5 m the slope of the outboard temperature spectrum becomes s t e e p e r , most l i k e l y due to the response f e a t u r e s of the t h e r m i s t o r . T h i s i n d i c a t e s t h a t the g l a s s c o a t i n g around the t h e r m i s t o r does i n h i b i t response and the t h e r m i s t o r s are net p e r f e c t t r a n s d u c e r s f o r the e n t i r e range of s c a l e s of i n t e r e s t . Also at about 5 m, the spectrum of the i n b o a r d t h e r m i s t o r begins to f l a t t e n . T h i s causes the s p e c t r a l r a t i o to i n c r e a s e , e x p l a i n i n g the shape of the g a i n curve ( f i g 5). At the very s m a l l s c a l e s , both s p e c t r a tend to f l a t n e s s and t h e r e f o r e the s p e c t r a l r a t i o w i l l tend towards 1 s i n c e both 51 s p e c t r a are about the same l e v e l . T h i s r e s u l t i s most l i k e l y due to the s i g n a l t o noise c h a r a c t e r i s t i c s o f the data l o g g i n g system. Of course there are the p o s s i b i l i t i e s t h a t t h i s f l a t t e n i n g r e s u l t s from some s m a l l s c a l e s t r u c t u r e , or a l i a s i n g of some higher frequency n o i s e but t h i s i s not b e l i e v e d t o be the case. The s p e c t r a are down about 60 db (a r a t i o of 10* i n value) and t h i s f i g u r e r e p r e s e n t s the s i g n a l to n o i s e r a t i o t h a t can be expected from the e l e c t r o n i c s of the r e c o r d i n g system and a l i a s i n g most l i k e l y won't occur because of the f i l t e r i n g before d i g i t i z a t i o n . Perhaps the e l e c t r o n i c s or time constant o f the inboard t h e r m i s t o r were s l i g h t l y d i f f e r e n t from those of the outboard t h e r m i s t o r or the r e c o r d i n g c o n d i t i o n s weren't as good f o r L f e w a s f o r T ^ ^ t o account f o r the d i f f e r e n c e s i n s m a l l s c a l e s p e c t r a l shape. Some f u r t h e r i n s i g h t may be gained by examining the coherence spectrum f o r the data ( f i g 7). Here the s o l i d h o r i z o n t a l l i n e i s the 95% s i g n i f i c a n c e l e v e l and the v e r t i c a l bars represent 95S confidence l i m i t s . The shape i s s i m i l a r to th a t o f the gain f a c t o r and i s g e n e r a l l y what one would expect, except perhaps f o r the r e l a t i v e l y high coherences a t s m a l l s c a l e s . T h i s might p o s s i b l y be e x p l a i n e d by re-examining the data l o g g i n g system. I f during r e c o r d i n g the s i g n a l s were not of s u f f i c i e n t amplitude, then i t i s p o s s i b l e that some noise would be i n t r o d u c e d . T h i s noise would be i n part the r e s u l t of v a r i a t i o n s i n the speed of the tape which c o u l d not be e n t i r e l y compensated f o r by the d i s c r i m i n a t o r ' s compensation u n i t , and would appear around 1 Hz or so. I f t h i s were the case, then the f noise would be mainly coherent n o i s e s i n c e a l l channels would be f i g . 7: Temperature coherence f o r the Indian Arm 5m data. 53 a f f e c t e d e q u a l l y . However i f the s i g n a l s were poorer so t h a t the noise l e v e l c f the e l e c t r o n i c s were reached before r e c o r d i n g , then i t i s p o s s i b l e t o have i n c o h e r e n t n o i s e . I t i s a l s o p o s s i b l e to have combinations of these two r e c o r d i n g c o n d i t i o n s j u s t d e s c r i b e d so t h a t a t the s m a l l s c a l e s two s i g n a l s might be coherent, p a r t i a l l y coherent or i n c o h e r e n t . Even i f one s e t s the r e c o r d i n g l e v e l s o p t i m a l l y one caniiot e x t r a c t s p e c t r a l l e v e l s s m a l l e r than 10- 6 of the l a r g e s t ones because of the o v e r a l l l i m i t of about 60 - 70 do s i g n a l t o n o i s e r a t i o . In most cases t h i s range i s achieved showing t h a t we have used the system to i t s l i m i t s . Superimposed on the f i l t e r i n g a c t i o n of the pump i s the e f f e c t of v a r i a t i o n s i n pumping speed. In removing the time l a g from the i n b o a r d data, an average t r a n s i t p e r i o d was used; t h i s average was c a l c u l a t e d using a m a j o r i t y o f the data runs. I t t h i s p e r i o d a c t u a l l y v a r i e d , then t h e r e c o u l d be some l o s s of coherence as i l l u s t r a t e d i n the f o l l o w i n y example. Suppose a patch of water with temperature T Q i s sensed by the outboard t h e r m i s t o r f o r time * t and i s pumped up the hose at speed V j j t h e l e n g t h of t h i s patch i n the hose i s given by v j ^ t . I f the speed of the water i n the hose changes from v^ to v^ b e f o r e the patch i s sensed by the inboard t h e r m i s t o r , then because the le n g t h of the patch remains the same, the time f o r which the patch i s measured by the inboard t h e r m i s t o r i s t= v ^ t / v ^ . . T h e r e f o r e the e f f e c t of t h i s patch w i l l appear at a d i f f e r e n t frequency i n the spectrum of the inboard t h e r m i s t o r . Pumping speed v a r i a t i o n s were as much as 20% of the mean but because of the averaging used i n a r r i v i n g at the s p e c t r a l r e s u l t s and the 54 f a c t t h a t the s p e c t r a were p l o t t e d a g a i n s t l e g frequency, t h i s speed v a r i a t i o n i s not l i k e l y to s e r i o u s l y a f f e c t the r e s u l t s . Moreover, s i n c e most of the sensors used f o r comparison are e s s e n t i a l l y at the same p o i n t i n the hose, the v a r i a t i o n w i l l have no e f f e c t cn t h e i r coherency. The r e s u l t s of examination of the data c o l l e c t i o n system r e v e a l that probably one can a t t a c h l i t t l e meaning to the r e s u l t s at s c a l e s s m a l l e r than about 10m. 4.3 Comment Cn S t a t i o n a r i t y Perhaps a comment on the s t a t i o n a r i t y of the s t a t i s t i c s i s i n order. I f the processes i n v o l v e d were s t a t i o n a r y , then the r e l a t i o n s h i p s between v a r i a b l e s would remain e s s e n t i a l l y the same. Eut i s t h i s r e a l i s t i c ? C o n s i d e r i n g the g e o p h y s i c a l f o r c e s at work and t h e i r v a r i a b i l i t y i n both t i n e and space, i t i s u n l i k e l y t h a t s t a t i o n a r i t y e x i s t s over l a r g e s c a l e s and time p e r i o d s . What about the s m a l l s c a l e s over a s i n g l e sampling run? Suppose we examine the r e s u l t s of subsampling some cf the data. Figure 8 shews coherence s p e c t r a f o r Indian Arm 5m t e m p e r a t u r e - c h l o r o p h y l l a June data which has been subsampled i n quarter s e c t i o n l e n g t h s of the o r i g i n a l d a ta. The o r i g i n a l data was 16 blocks l o n g , each block c o n s i s t i n g of 1024 data p o i n t s sampled at 4 hz. Here the coherences were c a l c u l a t e d f o r the f i r s t 4 b l o cks and then the next 4 and so on i n s t e a d of over the e n t i r e 16 b l o c k s . One can expect seme v a r i a b i l t y i n the l o n g e r s c a l e s because 1-5 JUNE 1.0 -i X O 3 o - 4 •0-1 5-e L O G f -3 L O G f l-0i O.S u 9 - 12 T — •2 -I 13-16 L O G -I L O G f f i g . 8; Temperature-chlorophyll coherences for the Indian Arm 5m data The n r i M n a 1 record was 16 blocks in length. Here the coherences are base™ on sucessJve ck lengths. The numbers i n the lower l e f t comer of the plots reprLLt the blocks t e d . 15 JUNE f i g . 9: Temperature-chlorophyll coherences f o r the Indian Arm 5m data where the o r i g i n a l record has been s e c t i o n e d i n t o 2 8-block p i e c e s . 57 of the s m a l l number of degrees of freedom i n the e s t i m a t e s , about 8 i n each of the f i r s t f o u r . Also i t must be remembered t h a t the l a s t few estimates w i l l not be r e l i a b l e because cf the n o i s e problems d i s c u s s e d i n s e c t i o n 4.2 above. I t appears t h a t the s p e c t r a are somewhat d i f f e r e n t . In p a r t i c u l a r , b l o c ks 13-16 have a s l i g h t l y . d i f f e r e n t coherence spectrum from the e t h e r s . I f we now s u b d i v i d e the o r i g i n a l data i n t o 2 s e c t i o n s of 8 blocks each ( f i g 9 ) , we see the s p e c t r a appear t o be d i f f e r e n t . F i g u r e 16 shows the TEMF-CHL A coherence spectrum f o r the e n t i r e 16 block r e c o r d and i s s i m i l a r t o those shown i n f i g u r e s 8 and 9, e s p e c i a l l y when the 95% c o n f i d e n c e l i m i t s are c o n s i d e r e d . Most of the v a r i a b i l i t y i n the s e c t i o n e d r e s u l t s i s between these l i m i t s and t h e r e f o r e w i t h i n s t a t i s t i c a l e r r o r . , What t h i s means i s t h a t although not completely s t a t i o n a r y , and showing more v a r i a b i l t y than would a Gaussian v a r i a b l e , the r e s u l t s are c o n s i s t e n t with what one would expect of g e o p h y s i c a l turbulence and encourages the use of t h i s technique of a n a l y s i s . 4.4 D i s c u s s i o n Of The Data I t i s probably wise to examine the r e s u l t s of i n d i v i d u a l data runs and g a i n a " f e e l " f o r the i n t e r a c t i o n s between the i measured parameters. The s m a l l e r s c a l e s can be s t u d i e d using s p e c t r a l a n a l y s i s and some i n f o r m a t i o n on the l a r g e r s c a l e s can be obtained by l o c k i n g at the average or zero freguency component of each data block t h a t was transformed. S t a t i s t i c a l l y i t i s much b e t t e r t o use data runs of long d u r a t i o n and t h i s a l s o allows us t o look a t l a r g e r s c a l e s . 58 Since the s h i p ' s p o s i t i o n was a l s o recorded as a f u n c t i o n c f time, the block averages can be d i s p l a y e d g e o g r a p h i c a l l y , and doing t h i s might a i d i n e x p l a i n i n g seme of the r e s u l t s . Most long data runs took plac e i n June and J u l y and these data w i l l be d i s c u s s e d i n i t i a l l y . The data run i n Indian Arm at 5m depth f o r the month of June i s a f a i r l y good example of the type of p a t c h i n e s s t h a t was measured and i s shewn as a f u n c t i o n c f time i n f i g 10. The s p e c t r a to be d i s c u s s e d are normalized i n the sense that the estimate f o r each band has been d i v i d e d by the area under the spectrum and t h e r e f o r e the spectrum x freguency i s non d i m e n s i o n a l . Table I c o n t a i n s the n o r m a l i z i n g f a c t o r s used f o r the v a r i o u s s p e c t r a and e x p l a i n s the symbols used as i d e n t i f i e r s . For most of the v a r i a b l e s the f a c t o r s vary only by a f a c t o r of 10, but f o r oxygen and s a l i n i t y the ranges are 2 and 3 decades r e s p e c t i v e l y . In order to compare ab s o l u t e l e v e l s cf the s p e c t r a , r e f e r e n c e l i n e s corresponding to an f"$ value of 1 0 - 3 i n the a p p r o p r i a t e u n i t s were p l a c e d on each s p e c t r a l p l o t . To compare the s p e c t r a a l l one need do i s superimpose these r e f e r e n c e l i n e s . Because of the wide range of f r e g u e n c i e s used i n the a n a l y s i s , i t i s convenient to use a l o g s c a l e on the freguency a x i s . T h i s has the e f f e c t of d i s t o r t i n g the shape cf the spectrum so that i t appears t h a t the lower f r e g u e n c i e s ( l a r g e r s c a l e s ) c o n t r i b u t e more to the v a r i a n c e than they a c t u a l l y dc. To show properly what the r e l a t i v e c o n t r i b u t i o n s are i t i s usual to p l o t i n s t e a d of a g a i n s t l o g f . 10.691 T E M P . °C. ^ ^ ^ ^ II.•0 J f ooom. d fe 8t;en 0ded' h e ° r i 8 i n a l *** ^  **** ^ * a t W " 8 P a s s e d . The oxygen trace has not b een 60 TABLE I NORMALIZING FACTORS Dataset + Temp. Tout S a l t 02 C h i . a wedge No. of Blocks (C«) 2 (C°) 2 (ml/1)2 (mg/m^) 2 (volt s ) 2 June 15-16 2.77E-02 3.60E-02 1.87E-01 2.44E-01 6.24E-01 *I5-16 2.77E-02 3.60E-C2 1.87E-01 3.29E-02 6.24E-01 •H5-11 7.55E-02 9.06E-02 6.01E-01 1.31E-02 2.92E-01 GS5-10 8.09E-02 9.64E-C2 8.79E-03 1.84E-03 3.05E-02 J u l y *H1-17 1.90E-01 2.30E-01 6.41E+00 2.41E-02 2.83E-02 GS1- 13 1.99E-01 2.22E-01 1.44E-01 3.43E-02 1.47E-01 GS3-19 7.49E-02 8.39E-02 2.46E+00 5.48E-02 2.31E-01 GS5-10 7.69E-02 7.85E-C2 2.27E-01 7.67E-03 2.28E-02 A p r i l 13-06 3.80E-02 8.301-02 2.00E-02 9.93E-0 2 4.55E-01 2.29E-01 15-11 * 4.33E-02 8.46E-02 1.27E-01 1.06E-02 8.08E-02 1.27E-01 May 31-06 2.98E-02 4.81E-02 5.83E-02 3.02E-02 1 .33E-02 B3-05 u 1.11E-02 1.96E-02 4.64E-01 1.98E-02 8.58E-02 Table I: A t a b l e of n o r m a l i z i n g f a c t o r s f o r the data t o be di s c u s s e d . An * i n d i c a t e s those runs where the oxygen data were detrended before the s p e c t r a were c a l c u l a t e d . Note the wide range of values f o r the s a l i n i t y data, probably dependent on the s t r a t i f i c a t i o n present during sampling. The very low oxygen values occur when the s i g n a l to n o i s e r a t i o was s m a l l and i s r e f l e c t e d i n the s p e c t r a l shape:at s m a l l s c a l e s . In the data s e t symbols the l e t t e r stands f o r the l o c a t i o n and the number f o r the nominal depth i n meters; that i s I stands f o r Indian Arm, H f o r Howe Sound, GS f o r Georgia S t r a i t (near the F r a s e r F i v e r mouth) and B f o r Bute I n l e t , eg. 15-16 i s from I n d i a n Arm at 5 meters depth and has 16 blocks of 1024 po i n t s sampled at 4 hz. v a r i a n c e - (f -"= j " f (f)df = J f f ( f ) d f = 2.30 f f f (f)dlogf 4.4.1 P l o t t i n g the spectrum a g a i n s t l o g d i s t a n c e merely s h i f t s the spectrum along the h o r i z o n t a l a x i s without changing the area underneath s i n c e : log distance = log( c/f ) 4.4.2 = log c* - log f = constant - log f d(log distance) = - dlog f 4.4.3 where c i s the average flow speed of the water past the pump i n t a k e . Therefore p l o t t i n g f${f) a g a i n s t d e c r e a s i n g l o g d i s t a n c e conserves the r e l a t i v e c o n t r i b u t i o n s to the v a r i a n c e as w e l l . I f there i s a l a r g e dynamic range, t h a t i s i f the estimates vary over a number of decades, then l o g i s p l o t t e d . Such a p l o t a l s o enables us t c lock f o r power law r e l a t i o n s h i p s . The area under the curve i s no longer p r o p o r t i o n a l to the v a r i a n c e , but i t i s s t i l l c l e a r where the r e l a t i v e c o n t r i b u t i o n s occur i n the spectrum. In comparing these r e s u l t s with those obtained by other authors i t must be remembered t h a t log"£ i n s t e a d of l o g f H i s o f t e n p l o t t e d . The slope of the r o l l - o f f of s p e c t r a d i f f e r s by 1 depending on the method. For example a -2 slope i n a log*5 vs. l o g f p l o t becomes a - 1 s l o p e i n a l c g f " $ vs, l o g f p l o t . The s p e c t r a were c a l c u l a t e d using f a s t F o u r i e r transform 62 techniques and standard d e v i a t i o n s of the s p e c t r a l values can be c a l c u l a t e d d i r e c t l y from the data r a t h e r than r e l y i n g on t h e o r e t i c a l d i s t r i b u t i o n s . The v e r t i c a l bars a s s o c i a t e d with each estimate r e p r e s e n t a band of 6855 confidence using the observed v a r i a n c e and assuming a ^ 2 d i s t r i b u t i o n . The l e n g t h of each bar i s determined i n part by the number of degrees cf freedom i n the estimate as w e l l as the i n t e r m i t t e n c y , or v a r i a b i l i t y between b l o c k s , of the estimate. The f i r s t few e s t i m a t e s were determined from block averages as d i s c u s s e d i n the previous chapter and no e r r o r based on the v a r i a b i l i t y i n tne data can be c a l c u l a t e d . i Indian Arm 5m - June F i g u r e s 6,11,12 show s p e c t r a f o r the Indian Arm 5 m data. They e x h i b i t s i m i l a r shapes except f o r the oxygen spectrum. They are red s p e c t r a , meaning that most of the v a r i a n c e i s at low f r e q u e n c i e s or l a r g e s c a l e s . The r o l l - o f f of f$, through the mid-bands roughly f o l l o w s a -2 slope corresponding to "§> <* f " 3 . I f we c o n s i d e r the f i l t e r e f f e c t of the hose, then the s l o p e at s c a l e s of about 10m i s steepened by -1 approximately. A s s y m p t o t i c a l l y the pump e f f e c t changes the s l o p e by -2 at the s m a l l e s t s c a l e s but here we have reached the system noise l e v e l . T h i s would mean t h a t our -2 s l o p e f o r f*$ r e a l l y i s about -1 so t h a t "5 * f " 2 and t h i s corresponds with the r e s u l t s of Denman (1974). S a l i n i t y and temperature f o l l o w each other f a i r l y c l o s e l y but temperature f a l l s o f f s l i g h t l y f a s t e r , p o s s i b l y due to sensor l i m i t a t i o n s . C h l o r o p h y l l e x h i b i t s an even steeper shape which i s probably due to the l i m i t e d response of the I 5 JUNE o.o 2.0 t.O LOG DISTANCE (M) -i.o f i g . 1 1 : C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the Indian Arm 5m data. The numbered slopes are f o r reference only and have not been f i t t e d . I 5 JUNE T 2.0 1.0 0.0 LOG DISTANCE (M) i.o 4.0 3.0 2.0 1.0 LOG DISTANCE (M) 0.0 -1.0. f i g 1 2 : The oxygen spectra for June Indian Arm 5m data. The upper plot is of the untreated data and the lower plot shows the spectrum of the detrended data. Differences are most noticeable in the SCOR low part of the spectrum. 65 i f l u o r o m e t e r and c o r r e c t i n g f o r t h i s e f f e c t the s l o p e would probably be much the same. I t i s wise at t h i s p o i n t to remember t h a t the instruments have d i f f e r e n t freguency response c h a r a c t e r i s t i c s as o u t l i n e d i n the chapter on i n s t r u m e n t a t i o n . Because c f the flow speed in the p i p e , the response of the s a l i n i t y probe i s probably good r i g h t out to the very s m a l l s c a l e s . I f the time constant of the t h e r m i s t o r improves to roughly 1/3 sec because of the f l e w , then its 3db or 1/2 power p o i n t w i l l be about 2m. The improvement p r e d i c t e d by simple theory ( as o u t l i n e d i n Chapter II ) is u n l i k e l y to occur because of the g l a s s c o a t i n g . The responses of the fluorcmefer and the oxygen probe are not as good. Eoth of these w i l l probably have 3 db p o i n t s , -"Jfobserved) = 1/2^(true) - at about 10 m to 20 m, i e . l o g d i s t a n c e = 1.0 to 1.3. Keeping t h i s i n mind then, the s l i g h t t a i l i n the c h l o r o p h y l l spectrum at s m a l l s c a l e s , i s most l i k e l y the r e s u l t of poor s i g n a l to noise c o n d i t i o n s at those f r e g u e n c i e s . There might also be some a l i a s i n g back c f noise that hasn't been f i l t e r e d out d u r i n g p r o c e s s i n g . The oxygen spectrum ( f i g 12) appears to f a l l o f f with a -1 s l o p e at the l a r g e s c a l e s and i s u n l i k e the other s p e c t r a . The small s c a l e s appear t c l e v e l o f f s l i g h t l y probably because the system n o i s e l e v e l has been reached. The l a r g e s c a l e r e s u l t s though are l i k e l y caused by the l a r g e t r e n d present i n the o r i g i n a l data ( f i g 10) s i n c e the spectrum of a trend with no other f l u c t u a t i o n s has a slope of -1 on a logfH vs leg f p l o t . Some of t h i s t rend may be due to the slow decrease i n probe s e n s i t i v i t y due to membrane aging. Only the mean e f f e c t of t h i s aging was removed i n the s i g n a l 66 p r o c e s s i n g . However the observed t r e n d f o r the 15 June data i s very much l a r g e r than what one would expect from membrane aging and i s probably a r e a l change. In t h i s sense the spectrum of the untreated data i s more r e a l : however i f one had a much longer record and the process were s t a t i o n a r y , t h i s t r e n d energy would appear as p a r t c f the c o n t r i b u t i o n s at s c a l e s l a r g e r than those r e s o l v e d . Because of the sample l e n g t h , energy has •leaked * and contaminated the spectrum. Thus the spectrum c f the detrended data may be more r e p r e s e n t a t i v e of what one would o b t a i n from r a t h e r l o n g e r r e c o r d s . Trend removal was done when necessary f o r the oxygen data. The spectrum c a l c u l a t e d a f t e r l i n e a r t rend removal i s shewn i n the lewer part of f i g 12. The shape of the mid and s m a l l s c a l e r o l l - o f f i s much the same as t h a t of trended data*s spectrum. Note though, that the s p e c t r a l shape of the very l a r g e s c a l e s has been a l t e r e d and i s now s i m i l a r to those s p e c t r a l shapes of the other parameters. The oxygen spectrum d i f f e r s from those s p e c t r a of other v a r i a b l e s i n the mid bands and the very s m a l l s c a l e s . The o r i g i n a l oxygen data do not appear to have as much a c t i v i t y i n the mid s c a l e s as the other data which might be n a t u r a l or perhaps there was a problem with the probe. There i s a l s o the p o s s i b i l i t y t h a t the 3db poin t f o r the oxygen probe corresponds to a l o g d i s t a n c e value of about 1.8 and so the s m a l l s c a l e s p e c t r a l r e s u l t s are the r e s u l t c f i n s t r u m e n t a t i o n response l i m i t a t i o n s coupled with poor s i g n a l to noi s e c o n d i t i o n s . The s a l i n i t y and temperature s p e c t r a have very s i m i l a r shapes. He see t h a t the l e v e l of £ $ at l a r g e s c a l e s i s j u s t 67 about constant and begins to decrease at about 50 m or so. The shape i s s i m i l a r t c t u r b u l e n t wind s p e c t r a where the dcwnwind component has a f l a t fH. spectrum near the r e g i o n of i n p u t of v a r i a n c e (Macdonald, 1972) and then drops o f f a t h i g h e r f r e q u e n c i e s . I f one t h i n k s of r e l a t i v e l y homogeneous patches of s a l i n i t y and temperature, t h i s r e s u l t simply means t h a t these patches are l a r g e r than about 50 m. The s l i g h t t a i l at the end of the s p e c t r a i s probably due to n c i s e . But s i n c e we are measuring i n t h e r m c c l i n e or h a l o c l i n e r e g i o n s where there i s a v e l o c i t y shear, i t i s n a t u r a l t o expect f l u c t u a t i o n s generated from these g r a d i e n t s i n the process cf some v e r t i c a l mixing. T h i s a c t i v i t y would tend to appear i n the s p e c t r a at s c a l e s over a decade or so centred on a s c a l e of about 20 times the depth c f the b r a c k i s h l a y e r i n Indian Arm. There w i l l a l s o be i n p u t s at even l a r g e r s c a l e s a s s o c i a t e d with h o r i z o n t a l g r a d i e n t s . Suppose we now go cn to examine the coherence r e l a t i o n s h i p s between parameters. The values from the SCOB-low a n a l y s i s have not been i n c l u d e d s i n c e they were not s i g n i f i c a n t enough. An examination of the o r i g i n a l d ata, f i g u r e 10, shows obvious coherences between the measured v a r i a b l e s . I f we p l o t the block averages, thereby removing the higher f r e q u e n c i e s i n the d a t a , we see s i m i l a r i t i e s i n the l a r g e s c a l e s as w e l l (see f i g u r e 13). There appears to be a 180 phase d i f f e r e n c e between the b i o l o g i c a l and p h y s i c a l parameters. T h i s r e l a t i o n s h i p with s a l i n i t y seems s u r p r i s i n g at f i r s t i f one assumes t h a t there i s no c h l o r o p h y l l a present i n the f r e s h water i n p u t to the i n l e t , because one might expect higher s a l i n i t i e s t o be a s s o c i a t e d with higher c h l o r o p h y l l counts and f r e s h e r water with lower values. INDIAN ARM 5m. JUNE 10 9 8 7 6 23.5 23.0 22.5 22.0 CHL. a rng/m 3 SALINITY 7oo 13r 12 8 3 3 m TEMP. °C r 1 ! ; 1 3 i P 1 C P ° f t h e b l o c k a v e r a 8 e s °r zero frequency component o Indian Arm data, e x c l u d i n g oxygen. 69 But t h i s e x p l a n a t i o n i s too s i m p l i s t i c as s h a l l be seen. F i g u r e s 14,15 shew p l o t s of block averages i n t h e i r g e o g r a p h i c a l l o c a t i o n s . Contouring i s u n f o r t u n a t e l y not f e a s i b l e although c e r t a i n l y d e s i r a b l e . The data were taken to the south of Croker I s l a n d but north of and away from the l o c a l i z e d e f f e c t s of the Buntzen power pl a n t d i s c h a r g e . Note that the lower s a l i n i t i e s are on the western s i d e of the i n l e t where we might expect the r i v e r to be. The western channel by Croker I s l a n d i s narrow and shallow and should be a r e g i o n of r e l a t i v e l y s t r o n g v e r t i c a l mixing and the v a l u e s r e f l e c t t h i s . F i g u res 16,17 shew the coherence s p e c t r a f o r the data with 95$ confidence bars c a l c u l a t e d a c c o r d i n g to the formula of s e c t i o n 3.5. He f i n d t h at c h l o r o p h y l l a appears g u i t e coherent with temperature, about 0.7, and s l i g h t l y l e s s coherent with s a l i n i t y . Oxygen and c h l o r o p h y l l are the l e a s t coherent c f the c h l o r o p h y l l - p h y s i c a l parameter combinations as might be expected because of the d i f f e r e n t shapes of t h e i r s p e c t r a . Temperature and s a l i n i t y appear to be the most coherent v a r i a b l e s , except at the very s m a l l s c a l e s . The phase r e l a t i o n s h i p s are the same as these of the very l a r g e s c a l e s . The r e s u l t s seem to i n d i c a t e a reasonably i n t i m a t e r e l a t i o n s h i p between the p h y s i c a l and b i o l o g i c a l worlds which can be i n t e r p r e t e d to mean the d i s t r i b u t i o n of c h l o r o p h y l l i s to a c o n s i d e r a b l e e x t e n t , determined by the dynamics of the i n l e t . The dynamics are i n turn dominated by the f r e s h water i n p u t to the system. The major sources of f r e s h water are the r i v e r at the head of the i n l e t , the Buntzen power generating p l a n t and the p e r i p h e r a l streams. Most of the snow that feeds these C R O K E R StLtn°f:PhiCal Pl°tS °f the blOGk a v e r a 8 e s o f the Indian Ann INDIAN ARM JUNE 5 m SALINITY % 5 0 0 M. C O L D W E L L • E A C H CROKER v ISLAND f i g . 15: Geographical p l o t s of the bl o c k averages of the Indian A m 5 s a l i n i t y data. .3 .0 3.0 2.0 _ J 1.0 _ l 0.0 2.0 i r 1.0 o . o L O G D I S T A N C E ( M ) -1.0 2.0 o 3 . 0 TEMP-CHL fi I 5 JUNE -1.0 -2/0 LU U_! I T O o a ' to-rn U 03 J a: a: Q_ a 3.0 2.0 1.0 _J 0.0 _ l cb CP cb cpcb i — f — r 2.0 1.0 0.0 L O G D I S T A N C E (M) -1.0 j -2.0 SRL7-CHL R I 5 JUNE -1 .0 -2.0 f i g . 16: Coherences of c h l o r o p h y l l w i t h temperature and s a l i n i t y f o r the Indian Arm 5m data. For a d e s c r i p t i o n of the confidence bands and s i g n i f i c a n c e l e v e l s , see Chapter I I I s e c t i o n 6. aes c r i p t x o n 0.0 PHASE (X10J •; i-b H> (TO, I—1 O CD o;. CD 3 O CO tt) - 1 co xi o H i O r t t r CD C 3 CD M 3 Q J H -0 ) 3 > 3 cn 3 0 3 r t C co IB.O _ l _ 36.0 0.0 COHERENCE I O I I — - « 1 — 8 1 -e 1 i—-e 1 0.5 1.0 r- ( 1 | j 1 J c <"5 z T m 8 (TO a CD CD — • r t CO CD 2 3 o CD Cu „ c O — X << TO CD i 3 r c Cu 0 1 r t 0 1 PHASE (XIO1 ) 10.0 0.0 [B.O 0.0 1 1 . L COHERENCE 0.5 1.0 i e — 4 i — e — i i e 1 -e- -e 1 i — e — i i — n r - JB .O PHASE (X101 ) .0.0 1B.0 0.0 J COHERENCE i — e — i i—e— i i o I i — e — i t-e-H i o I I O I 0.5 1.0 I H I H c » 5 o.o PHASE (X1D1 J. 18.0 _1_ 36.0 0 ^ COHERENCE i e — i -e 1 0.5 _1_ 1.0 P I 74 p e r i p h e r a l streams would have melted by June and so t h i s l a s t source cf f r e s h water i s not s i g n i f i c a n t . The outflow from the power s t a t i o n d i s charge i s q u i t e l o c a l i z e d ( G i l m a r t i n , 1960) and u n l i k e l y to be a f a c t o r i n the area where the measurements took p l a c e . Thus the Indian River w i l l be the major source of f r e s h water and t h e r e f o r e r e s p o n s i b l e f o r the gross c i r c u l a t i o n of the i n l e t , The shear generated by the outflow of f r e s h water w i l l be the source of most of the mixing. F i g u r e 18 shows discharge curves f o r the r i v e r f o r the years 1958, 1959 ( a f t e r G i l m a r t i n , 1960) and we see t h a t the shear w i l l be l a r g e r during June than at ether t i n e s and t h e r e f o r e be mere of a f a c t o r i n the determination of the upper l a y e r dynamics. The e f f e c t s of the t i d e are mainly f e l t at the entrance to Indian Arm where th e r e i s a shallow s i l l and presumably some mixing occurs. Otherwise, there i s no a p p r e c i a b l e t i d a l e f f e c t except f o r the r a i s i n g or lowering of the s u r f a c e of the i n l e t . The winds, i f they were strong enough and blew long enough cou l d a f f e c t the near s u r f a c e l a y e r but were not s t r o n g i n t h i s case. F i g u r e 19 i s a diagram showing the average d a i l y winds measured at the l o c o m e t e o r o l o g i c a l s t a t i o n . The p r e s e n t a t i o n i s only of north or south winds s i n c e by i t s g e o g r a p h i c a l alignment the i n l e t i s r e l a t i v e l y s h e l t e r e d from east-west winds. The highest recorded wind speed was 10 knots, while the mean speed was l e s s than 2 knots and i t i s not thought t h a t the d i s t r i b u t i o n of plankton a t 5 m w i l l be a f f e c t e d g r e a t l y . We can conclude then that the most important p h y s i c a l f o r c e a c t i n g i n the d e t e r m i n a t i o n of upper l a y e r dynamics w i l l be the M J 5 N J M M J S N — J M M 1358 Si" 1 8> D l s c h a r § e of the Indian R i v e r f o r the years 1957-59 taken from G i L n a r t i n ^ U s u a l l y the outflow i s q u i t e high during the month of June when the data were taken. 76 -* 5.0-1 Q CD > < 2.5 WINDS AT I0C0 10 12 16 ~~r~ it ~ i— 20 - I 22 DATE IN JUNE f i g . 19: A plot of the average daily wind measured at the loco meteorological station located near the entrance of Indian Arm. Because of the geographical alignment of the inlet, only the north-south components were used 77 r i v e r . I f there i s no c h l o r o p h y l l i n the incoming r i v e r water then we might expect that any towed sampler would r e c o r d p a t c h i n e s s simply because the s a l t water c o n t a i n s plankton and the f r e s h does not and we might expect an in-phase r e l a t i o n s h i p between s a l i n i t y and c h l o r o p h y l l . But at the poi n t where the data were measured, there would have been ample time f o r the c h l o r o p h y l l to have been thoroughly mixed, and develop. What i s important i s the v e r t i c a l d i s t r i b u t i o n of c h l o r o p h y l l . In Indian Arm most of the production takes place i n the top 5 m or so ( G i l m a r t i n , 1960) and u s u a l l y the v e r t i c a l d i s t r i b u t i o n w i l l net be homogeneous but i n c r e a s e away from the s u r f a c e , go through a maximum and then decrease with depth. Probably a c h l o r o p h y l l maximum e x i s t s at some l e v e l above the 5 m sampling depth. Data taken a t a depth of 3 m i n d i c a t e higher c h l o r o p h y l l values than at 5 m. Therefore i n r e g i o n s where there i s s t r o n g v e r t i c a l mixing we might expect to f i n d higher values of c h l o r o p h y l l at 5 m than i n regions were no mixing takes p l a c e . Strong v e r t i c a l mixing w i l l occur where there are l a r g e shears and t h e r e f o r e i n those areas where the r i v e r d r i v e n flow i s s t r o n g e s t . Therefore we might a s s o c i a t e higher c h l o r o p h y l l values with lower s a l i n i t i e s . T h i s f e a t u r e can be f u r t h e r g e n e r a l i z e d . The phase r e l a t i o n s h i p between two parameters w i l l be determined by the s i g n s c f t h e i r g r a d i e n t s at the sampling depth. In a d d i t i o n , the coherence w i l l be determined by the shapes of the v e r t i c a l d i s t r i b u t i o n s of the v a r i a b l e s . For example i f one parameter i s f a i r l y homogeneous and another h i g h l y s t r a t i f i e d , mixing w i l l 78 not a l t e r the f i r s t very much but night a f f e c t the second a great d e a l . T h e i r s i g n a l s would show d i f f e r i n g amounts of a c t i v i t y and we would thi n k that t h e i r coherence would be l e s s than i f both v a r i a b l e s were s t r o n g l y s t r a t i f i e d . Let us now re-examine the coherence s p e c t r a keeping i n mind the s p e c t r a l shapes of the parameters and the l i m i t a t i o n s imposed by the Instrumentation and sampling method. There appears to be a f a i r l y s trong r e l a t i o n s h i p between o temperature and c h l o r o p h y l l . They are 180 out of phase which given the s i g n c f the c h l o r o p h y l l g r a d i e n t means that temperature i s i n c r e a s i n g away from the s u r f a c e of the i n l e t . T h i s deduction seems reasonable s i n c e the f r e s h water input w i l l be mainly the r e s u l t of snow melt. The apparent d i p s i n the coherence spectrum are not s i g n i f i c a n t s i n c e a s t r a i g h t l i n e can be drawn through a l l the estimates or t h e i r e r r o r b a r s . The f a c t t h a t the phase appears to be c o n s i s t e n t l y 180° i n c o n j u n c t i o n with r e l a t i v e l y high coherence at the very s m a l l s c a l e s p o s s i b l y i n d i c a t e s that the n o i s e i s to some extent not random and perhaps i s tape n o i s e as d i s c u s s e d above. Random noise would l i k e l y appear below the 95% s i g n i f i c a n c e l i n e and the phase es t i m a t e s would not be c o n s i s t e n t l y the same. This reasoning assumes t h a t the s i g n a l s at the very s m a l l s c a l e s are indeed n c i s e , which the s p e c t r a l shapes appear to c o n f i r m . Because of the s i m i l a r i t i e s i n shape of the temperature and s a l i n i t y s p e c t r a , we expect the SALT-CHL A coherence t o be s i m i l a r to the TEMP-CHL A coherence. In f a c t the appearance i s almost i d e n t i c a l except that the o v e r a l l l e v e l s are lowered. The TEMP-SALT coherence i s q u i t e high, about 0.9, at l a r g e 79 s c a l e s and then begins to decrease at about l o g d i s t a n c e = 1. T h i s i s probably a n a t u r a l decrease as the s c a l e s s h o r t e n . At the very s m a l l s c a l e s the phase becomes e r r a t i c which i s a l s o an i n d i c a t i o n of la c k of a s s o c i a t i o n between parameters. The p l o t s of coherence i n v o l v i n g oxygen are a l l s i m i l a r i n shape. The observed coherence i s f a i r l y h igh, about 0.7, a t the l a r g e s c a l e s and then drops r a p i d l y at l o g d i s t a n c e 1.2 - 1.5. Th i s s c a l e i s about the same as t h a t at which the oxygen spectrum ( f i g 12) changes to a slope of about 0.5 and most l i k e l y the oxygen system noise l e v e l i s being approached, which would account f o r the drop i n oxygen coherence at s m a l l e r s c a l e s . The comment was made above concerning the lack of i n t e r m e d i a t e f r e g u e n c i e s i n the o r i g i n a l data and perhaps that i s why the l e v e l s c f coherence are sc low through the mid-bands. T h i s apparent l a c k of s i g n a l through the mid-band f r e g u e n c i e s may account f o r the d i f f e r e n t s p e c t r a l shape. This behaviour might r e s u l t from problems with membrane degradation or e l e c t r o d e f o u l i n g so that the probe was net s e n s i t i v e at those f r e g u e n c i e s . i i Howe Sound 5m - June He can compare the June Indian Arm data with t h a t taken at the same depth i n Howe Sound approximately f o u r days e a r l i e r . The r e c o r d l e n g t h i s s h o r t e r f o r the Howe Sd d a t a , only 11 blocks as compared with 16 f o r the Indian Arm data. Immediately n o t i c e a b l e from p l o t s of block averages ( f i g u r e 20) i s that the average value of c h l o r o p h y l l i s l e s s than that i n I n dian Arm, and th a t the v a r i a b i l i t y i n the c h l o r o p h y l l f i e l d 80 HOWE SOUND 5m JUNE 4 " 3 ~ 2 L 20 .0 -19 .0 " 18.0-17 .0 L CHL. a mg/rrr S A L I N I T Y °/oo 13 12 1 1 1 -TEMP. °C ' 3J7 m. f i g . 20; P l o t s of bl o c k averages f o r the June, Howe Sound 5m data. 81 i s not as gre a t . The average s a l i n i t y i s l e s s than t h a t of the Indian Arm data so th a t the e f f e c t s of the r i v e r are f e l t more i n Howe Sound. The r i v e r flow i n t o t h i s i n l e t i s g r e a t e r than that i n t o Indian Arm and a l s o these data were measured nearer the head of the i n l e t than the Indian Arm data. The s p e c t r a ( f i g s . 21,22,23) show s l i g h t l y d i f f e r e n t l a r g e s c a l e shapes than the Indian Arm data. The l a r g e r s c a l e s do not e x h i b i t so much a p l a t e a u as a r o l l - o f f l e a d i n g t c another source of variance at roughly 100 m. The r i s e i n the s p e c t r a at t h i s s c a l e i s most n o t i c e a b l e i n the s a l i n i t y spectrum. T h i s r i s e might p o s s i b l y be an i n t e r n a l wave e f f e c t or g e n e r a t i o n c f v a r i a t i o n s by the v e r t i c a l shear. Beyond t h i s s c a l e s i z e , the r o l l - o f f c h a r a c t e r i s t i c s are s i m i l a r to each other and to the Indian Arm data except t h a t the Howe Sd, c h l o r o p h y l l spectrum does not r o l l o f f g u i t e as s t e e p l y as the Indian Arm spectrum. The major d i f f e r e n c e s between the s e t s of s p e c t r a are i n the oxygen s p e c t r a . The Howe oxygen spectrum does not e x h i b i t the same tendency t c f l a t t e n i n the mid-band r e g i o n (at about 5-10m) . At the very sma l l s c a l e s , the s p e c t r a e x h i b i t s i m i l a r l e v e l l i n g as the noise l e v e l of the system i s reached. The temperature - c h l o r o p h y l l coherence ( f i g 24) i s f a i r l y h i gh, between 0.6 and 0.7, but f o r s c a l e s of 20-50 m drops below the 9595 s i g n i f i c a n c e l e v e l . The high coherence of the l a r g e r s c a l e s i s r e f l e c t e d i n the p l o t s of block averages ( f i g 20) where i t appears that the temperature and c h l o r o p h y l l p l c t s mirror each other. That s a l i n i t y and c h l o r o p h y l l are r e l a t e d at the l a r g e s c a l e s i s not so immediately obvious from the block averages and i t i s not s u r p r i s i n g t h a t the SALT-CHL A coherences H5 JUNE f i g . 21: Temperature s p e c t r a f o r the Howe Sound 5m data. H 5 JUNE 4.0 T 3.0 2.0 1.0 0.0 LOG DISTANCE (M) -1.0 f i g . 2 2 : C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the Howe Sound 5 m data. H5 JUNE 4.0 T 3.0 T r 2.0 1.0 LOG DISTANCE (M) o.o f i g . 23: The spectrum of the detrended oxygen data from Howe Sound 5m measured in June. 85 are a b i t lower than the TEHP-CHL fl coherences f o r s c a l e s g r e a t e r than 100 ra. Eetween 100 m and 10 m however, the observed SA1T-CHL A coherences are about 0.75; higher than the l a r g e r s c a l e v a l u e s . A l s o , the oxygen - c h l o r o p h y l l ccherences are high out to about l o g d i s t a n c e = 1.2 and the s a l i n i t y -oxygen coherence values are high f o r a l l s c a l e s . Yet temperature coherences with s a l i n i t y and oxygen are b a s i c a l l y i n s i g n i f i c a n t f o r a l l s c a l e s shown i n the coherence s p e c t r a . Perhaps these r e s u l t s w i l l be b e t t e r understood i f we l o c k ar the nature of the p h y s i c a l environment. In Howe Sound, near the head of the i n l e t , the f r e s h water outflow from the Sguamish r i v e r , r e t a i n s i t s i n t e g r i t y f o r a f a i r d i s t a n c e down i n l e t (see f i g 38). Suppose t h a t the b r a c k i s h r i v e r water i s at a d i f f e r e n t temperature from the other i n l e t waters but t h a t the temperature f i e l d i s v i r t u a l l y v e r t i c a l l y homogeneous everywhere. The s a l i n i t y and oxygen f i e l d s are v e r t i c a l l y s t r a t i f i e d , s a l i n i t y i n c r e a s i n g away from the s u r f a c e , oxygen decreasing but n e i t h e r e x h i b i t l a r g e h o r i z o n t a l d i f f e r e n c e s . The c h l o r o p h y l l d i s t r i b u t i o n i s h o r i z o n t a l l y v a r i a b l e and a l s o has some v e r t i c a l s t r u c t u r e with a maximum above the sampling depth of 5 m. I f t h i s d e s c r i p t i o n of the environment e x i s t e d and i f the s h i p were steaming through the path of the r i v e r and then cut again, then the very l a r g e s c a l e s would show temperature f l u c t u a t i o n s t hat were coherent with c h l o r o p h y l l but not with s a l i n i t y or oxygen. At s m a l l e r s c a l e s , l e s s than 100 m, a s i t u a t i o n s i m i l a r to that d i s c u s s e d concerning the I n d i a n Arm 5 m data i s achieved. The coherences and phases obtained can be accounted f o r because of the v e r t i c a l s t r u c t u r e cf the t X K X >c / *1 1 1 — 0 1.0 0.0 -1.0 LOG DISTANCE (M) -2.0 o UJ in cc x tt-n * d) 3-0 2.0 1.0 0.0 -1 0 LOG DISTANCE (M) f i g . 25: Coherences f o r the Howe Sound 5m d a t a . -2.0 88 parameters and the v e r t i c a l mixing o c c u r i n g i n the r i v e r -c o n t r o l l e d flow regime. For s c a l e s l a r g e r than 100 m but l e s s than those of a k i l o m e t r e or so, t h e r e must be some o v e r l a p of t h e v a r i a n c e producing processes s i n c e c h l o r o p h y l l i s coherent with a l l three ether v a r i a b l e s between 100 m and about 250 m. To summarize, the v a r i a b i l i t i e s may have been caused by d i f f e r e n t p h y s i c a l mechanisms; the very l a r g e s c a l e s caused by t h e s h i p ' s path through the d i f f e r e n t regimes of the r i v e r c o n t r o l l e d flow and the other i n l e t waters; the s m a l l e r s c a l e s r e s u l t i n g from v e r t i c a l t u r b u l e n c e . T h i s e x p l a n a t i o n i s c o n s i s t e n t with the s p e c t r a l shapes. The temperature spectrum shows a trend towards higher v a r i a n c e at the very l a r g e s c a l e s ( > 1000 m) but does not h i n t a t a source of v a r i a n c e around l o g d i s t a n c e = 1.5 as does the s a l i n i t y spectrum. The c h l o r o p h y l l spectrum i s r e l a t i v e l y f l a t around t h i s s c a l e ( l o g d i s t = 1.5) but a l s o shows a t r e n d tc higher v a r i a n c e i n the SCCE-low s t a t i s t i c s whereas t h i s f e a t u r e i s not so n o t i c e a b l e i n the s a l i n i t y spectrum. I t i s d i f f i c u l t to say i f the oxygen spectrum mimics t h a t of s a l i n i t y at about 30 m or not, perhaps because the instrument's response i s beginning to r c l l o f f . From the s p e c t r a i t i s seen t h a t the system noise l e v e l s are net reached u n t i l about 5 m f o r any of the parameters, yet we must account f o r the high coherences present i n the data f o r s c a l e s c f order 10 m. Also there i s a d i p i n the c h l o r o p h y l l coherence with s a l i n i t y c e n t r e d around l o g d i s t a n c e = 1.2 to 1 . 4 . T h i s d i p i s perhaps a s s o c i a t e d with the peak i n the s a l i n i t y spectrum and t h i s ' e x t r a ' v a r i a n c e i s not w e l l r e l a t e d 89 to c h l o r o p h y l l . There a l s o e x i s t s the p o s s i b i l i t y t h a t the pump and hose system c o u l d be c r e a t i n g some s t r u c t u r e a t the s m a l l e r s c a l e s which could be coherent and so the noise spectrum i s not reached so g u i c k l y . Eecause the s p e c t r a do not i n d i c a t e low s i g n a l tc noise r a t i o s f c r the i n s t r u m e n t a t i o n , i t i s not b e l i e v e d that the high coherences near 10m are the r e s u l t of a coherent noise phenomenon although at s c a l e s l e s s than about 5m t h i s noise c c u l d be important. S t i l l i t i s d i f f i c u l t to determine e x a c t l y what i s happening and i t i s probably wise to ig n o r e the very s m a l l s c a l e ( < 10 m) r e s u l t s . I f one rexamines some aspects of the coherence r e s u l t s e s p e c i a l l y these i n v o l v i n g temperature, s a l i n i t y and c h l o r o p h y l l , one might not b e l i e v e the nature cf the r e l a t i o n s h i p s shown i n the r e s u l t s . For example both temperature and s a l i n i t y are 180 degrees out of phase with c h l o r o p h y l l yet are a l s o mainly 180*degrees out of phase with each et h e r . In a d d i t i o n the l e v e l s of coherence dc net appear c o r r e c t f o r temperature and s a l i n i t y s i n c e both are f a i r l y w e ll r e l a t e d t o c h l a at the l a r g e r s c a l e s but not with each o t h e r . T h i s can be e x p l a i n e d by the nature of the o r i g i n a l data which showed a phase change f o r the temperature data's r e l a t i o n s h i p with the s a l i n i t y during the data run. T h i s change of phase i s the cause of the low coherences and i s probably a r e s u l t of the d i f f e r e n t p h y s i c a l regimes as d i s c u s s e d above. Although a s i m i l a r s i t u a t i o n e x i s t e d between temperature and c h l o r o p h y l l , the c o n t r i b u t i o n s from the temperature data f o r t h i s occurence of a phase change were s m a l l and so d i d not a f f e c t the t e m p e r a t u r e - c h l o r o p h y l l a r e l a t i o n s h i p . 90 i i i Georgia S t r a i t 5m - June The Georgia S t r a i t data are i n t e r e s t i n g because the r e s u l t s show the e f f e c t s of s h i p motion. The s p e c t r a ( f i g s . 26,27,28) of every v a r i a b l e except c h l o r o p h y l l show a peak a t a freguency corresponding to a p e r i o d of about 6 sec which i s a s u r f a c e wave p e r i o d . I t was a b i t "bouncy" when these data were obtained. The peak i s most pronounced i n the s a l i n i t y spectrum where the g r a d i e n t might be the mcst severe and does not appear i n the c h l o r o p h y l l spectrum which perhaps i n d i c a t e s a r e l a t i v e l y v e r t i c a l l y homogeneous c h l o r o p h y l l f i e l d . The shape of the oxygen spectrum i s p e c u l i a r and i s symptomatic of very poor s i g n a l to noise c o n d i t i o n s . The t a b l e of n o r m a l i z i n g f a c t o r s (page 60) shows t h a t the v a r i a n c e of these oxygen data was very s l i g h t , dcwn a f a c t o r of 10 from r e s u l t s already d i s c u s s e d . These c o n d i t i o n s mean t h a t the n o i s e spectrum i s reached e a s i l y . The climb i n the t a i l c f the spectrum i s c h a r a c t e r i s t i c of u n f i l t e r e d white noise p l o t t e d as logf3t-logrf . The subseguent l e v e l l i n g and descent r e s u l t s because of the f i l t e r i n g done i n s i g n a l p r e p a r a t i o n . The coherence r e s u l t s ( f i g s . 29,30) show the same peak as the v a r i a n c e s p e c t r a except when c h l o r o p h y l l i s one of the parameters. The l a c k of t h i s peak coupled with the r a t h e r low coherences at the higher f r e g u e n c i e s confirms our s u s p i c i o n s t h a t the c h l o r o p h y l l f i e l d i s reasonably v e r t i c a l l y homogeneous. The poor coherences with oxygen except at the motion freguency are i n d i c a t i v e of the poor s i g n a l c o n d i t i o n s except a t the l a r g e s c a l e s . In g e n e r a l coherences are comparatively lower than these cf previous r e s u l t s . 2.0 1.0 LOG DISTANCE (M) f i g . 26: Temperature s p e c t r a f o r June, Georgia S t r a i t 5m data. The peaks at about log distance =1.0 r e f l e c t wave a c t i o n . G.S. 5 JUNE CHL fi f i g . 27: C h l o r o p h y l l and s a l i n i t y s p e c t r a f o r the Georgia S t r a i t 5m data. G.S. 5 JUNE 2.0 1.0 L O G D I S T A N C E (M) r o.o i . o f i g . 28: The oxygen spectrum f o r Georgia S t r a i t 5m data. Trend d i d not appear to be a problem f o r these oxygen data and was not removed before c a l c u l a t i n g t h i s spectrum. The spectrum at the very s m a l l s c a l e s i s the noise spectrum, r i s i n g c h a r a c t e r i s t i c a l l y w i t h a +1 slope before r o l l i n g o f f as the analog f i l t e r i n g takes e f f e c t . .3.0 UJin U J X o o o a' to. cn UJ cn cn x 0_ 2.0 1.0 0.0 ep <P cb 3.0 f i g -t cpcp (p CP cp CP CP cb <fc end?. (feh -1.0 J TEMP-CHL fl 8 . S . 3 JUNE -2.0 2.0 1.0 0.0 LOG DISTANCE (M) .3.0 O •z. UJin U J X o a cn — oo _| UJ cn cx X Q_ o • 1 CP cpcp epep CP CP cb cb c)c5} -l.O J SflLT-CHL fi G. S . 9 JUNE -2 .0 -KO -2.-0 3.0 29: O i l o r o p h y l l coherences w i t h temperature and s a l i n i t y f o r June Georgia S t r a i t data taken at 5m 1 2.0 l.O 0.0 - l .O LOG DISTANCE (M) -2 .0 .3.0 UJ <_• z X o (_) 2.0 _ l 1 .0 _ l 0.0 _ l o Xr UJ CO <x X Q-c cb cb 'dicbci 3.0 3.0 ~~1 1 1 2.0 1.0 0.0 LOG DISTANCE (M) UJ UJ"1 o 2.0 _ _ l 1.0 l 0.0 I o UJ to cr x (Pr--t) ()' 4>L (M) a I i — i r 3.0 2.0 1.0 0.0 LOG DISTANCE (M) -] .0 _i TEMP-SRUr o.s. g JUNE -2.0 -1.0 -1.0 _ l TEMP-02 8. 8. S J U N E -1.0 -2.0 -2.0 -2.0 ,3.0 UJ CJ z UJ"1 or a" UJ X o (_) 2.0 _ J 1.0 _J 0.0 _J UJ CO cr x o_ 3.0 ,3.0 UJ (_) z Ujm , X a o 2.0 2.0 _ l 1 1.0 0.0 LOG DISTANCE (M) 1.0 _ j 0.0 L _ o UJ CO CI X r r r 3.0 2.0 1.0 o.o LOG DISTANCE (M) -1.0 SRLT-02 O . S . 8 J U N E -2.0 I -1.0 -3.0 I -2.0 -2.0 32-CHL fi e. s. s J U N E -3.0 -2.0 f i g . 30: Coherences f o r the Georgia S t r a i t 5m data. Note the peaks which are probably the r e s u l t of wave a c t i o n moving the sensing apparatus. S6 The r a t h e r w e l l d e f i n e d peak i n the s p e c t r a c f the v a r i a b l e s i s a good example of one of the problems of h o r i z o n t a l l y sampling with a f i x e d system, r i g i d l y a t t a c h e d t c a platform which i s wave s e n s i t i v e . In the presence of v e r t i c a l s t r u c t u r e , with the sampler moving s i n u s o i d a l l y through the water, the data recorded w i l l be a combination of v e r t i c a l and true h o r i z o n t a l s t r u c t u r e . Even i f t h e r e are no s u r f a c e waves, i n t e r n a l waves w i l l produce the same r e s u l t , moving the s t r u c t u r e up and down past the sensor. For example, f o r the Indian Arm June data, the average c h l o r o p h y l l value at the 3 m l e v e l was about two times the average value at the 5 m l e v e l , 13 mg/m3 compared to 8 mg/m3. I f we i n t e r p o l a t e l i n e a r l y as a f i r s t approximation to the c h l g r a d i e n t , then we have a change of .027 mg/m3 per cm. In the 5 m data some c f the l a r g e r s c a l e changes were 1 mg/m3. T h i s c o u l d be accomplished with a mere 37 cm ex c u r s i o n from the sampling depth, and could e a s i l y be managed i n a wave f i e l d i n Howe Sound or Georgia S t r a i t . These e f f e c t s are even more complicated i f the gra d i e n t i s n o n - l i n e a r , as i t probably i s . Care must be taken i n i n t e r p r e t i n g data sampled with the method used here. i v Howe Sound 1m - J u l y L e t us new l o c k at some r e s u l t s from 1 m i n Howe Sound f o r the month of J u l y . The block averages are shown i n f i g u r e 31 and we note the absence of c h l o r o p h y l l v a r i a b i l i t y over the l a r g e s c a l e s . The s p e c t r a ( f i g s . 32,33,34) are s i m i l a r to those data p r e v i o u s l y presented i n t h a t the temperature and 97 HOWE SOUND 1m JULY CHL. a mg/'m3 101-• i 1 647 m. f i g . 31: P l o t s of block averages f o r Howe Sound lm data.'Down-inlet i s to the r i g h t i n the p l o t s . 98 H 1 JULY H 1 JULY 101 s a l i n i t y s p e c t r a appear to have a knee i n them at about l o g d i s t a n c e - 1. T h i s knee c c u l d r e p r e s e n t the same source of variance as the bump at l o g d i s t a n c e = 1 i n the June H-5 data presented above but the source appears i n t h i s H-1 data with l e s s i n t e n s i t y . I f t h i s v a r i a n c e i s the r e s u l t of v e r t i c a l shears then t h i s decrease i n l e v e l should be expected s i n c e the g r e a t e s t shear i n Howe Sound w i l l occur a depth c l o s e r t o 5m than 1m. The T T 6 n p spectrum does not e x h i b i t as pronounced a knee as TTowT because of the f i l t e r i n g a c t i o n of the pumping system. A f t e r the knee, the r o l l - o f f i s with the same -2 s l o p e f o r f j , as i n the other s p e c t r a which would be a -1 slope approximately i f we c o r r e c t f o r the f i l t e r i n g e f f e c t of the hose. But even t h i s c o r r e c t i o n would not remove the knee s i n c e the s l o p e i n the spectrum before the knee i s -0.5. T h i s i s very s i m i l a r t c what Denman (1974) has r e p o r t e d as p o s s i b l y r e s u l t i n g from an i n t e r n a l wave f i e l d . The coherences ( f i g u r e s 35,36) of seme of the parameters do e x h i b i t a s l i g h t bump about t h i s frequency so t h i s e x p l a n a t i o n seems p l a u s i b l e . The oxygen spectrum has a p e c u l i a r shape, with a s l i g h t hump i n the 20-90 m range before i t descends i n t o the n o i s e at roughly 5 m. The bump i n the oxygen spectrum appears near the same s c a l e as the knee i n the temperature and s a l i n i t y s p e c t r a . Because the l a r g e r s c a l e oxygen spectrum f a l l s o f f more q u i c k l y than the other s p e c t r a , a source of v a r i a n c e at about l o g d i s t a n c e = 1.6 would appear as a bump i n the oxygen spectrum but as a knee i n the other s p e c t r a . Despite the presence of a s u r f a c e wave f i e l d d u r i n g sampling there are no peaks i n the s p e c t r a or coherences . 3 .0 3.0 2.0 I 1.0 _J 0.0 _J CP cp 1 1 2.0 1.0 0.0 L O G D I S T A N C E (M) -1.0 j -2.0 TEHP-CHL A H I JULY -1 .0 .3 .0 2.0 I UJ o UJtn X o o a cn' -2.0 o .—j a' UJ CO cr X 0 3 • — i . i 1.0 0.0 - J L _ $ cb (M>. CP CP CP 3.0 T 1 • 1 2.0 1.0 0.0 L O G D I S T A N C E (M) f i g . 35: Coherences of c h l o r o p h y l l w i t h temperature and s a l i n i t y f o r the Howe Sound lm data. -1 .0 _J - 2 . 0 SRL7-CHL R H I JULY - 1 .0 -2.0 M l 0 0 s-fD M CD 0 O n> CO Mi O H ? fD EC CD C/3 O § H " 3 C L P> rt a CD C O — I JD o .-PHASE IX10' 1 n n COHERENCE iB.O 0.0 13.0 0.0 0.5 I J . I I 1-- e -h-—e-1 "8- ' e -t , i — e — H i' to ' I 1 1 j 1 t — 1 » ] 1 1 i 1—J 1 5"? PHASE U10» ) COHERENCE 0 0 IBJjl 36.0 3JJ O.S l.O Q CO 2"° C O X ) 2 : o m 0 -e-- e -_ i _ ^ c i a c - £ x> PHASE (X10» ) COHERENCE 0 0 18.0 3C.0 0.0 O.S 1.0 Q CD E £ C O — I D z o i0 NT -s--e-— e — i 1 n n PHASE IX10 1 ) COHERENCE 0.0 IS.O 3C.0 0.0 O.S l.O |_w w J f -Q CD C O —I D O m o ffi i i - f - t i r- i a eoi a s s o c i a t e d with the s h i p motion s c a l e d i s c u s s e d above (GS 5m). T h i s would appear t o be evidence f o r some v e r t i c a l homogeneity i n the v a r i a b l e s at l e a s t near the s u r f a c e . The in-phase r e l a t i o n s h i p between s a l i n i t y and c h l o r o p h y l l a might be evidence c f t h e i r g r a d i e n t s having the same s i g n , but co u l d a l s o be the r e s u l t of h c r i z c n t a l v a r i a t i o n with l i t t l e l o c a l v e r t i c a l g r a d i e n t . The data were taken very near the head of the i n l e t and i t i s p o s s i b l e that with the r i v e r m a i n t a i n i n g i t s c o n t i n u i t y , mixing has not cccured s u f f i c i e n t l y so t h a t the f r e s h e r water w i l l have l e s s c h l o r o p h y l l than the s a l t i e r , g i v i n g a 0° phase r e l a t i o n s h i p . f i g u r e s 37 and 38 are g e o g r a p h i c a l p l o t s of the block averages cf c h l o r o p h y l l and s a l i n i t y . The path of the r i v e r i s e a s i l y f o l l o w e d as i t appears to maintain i t s e l f f o r g u i t e a d i s t a n c e downstream. But the c h l o r o p h y l l d i s t r i b u t i o n i s h o r i z o n t a l l y homogeneous. I t i s p o s s i b l e the str o n g winds blowing up i n l e t , with speeds of about 20 knots, and the wave f i e l d c r e a t e d by them e f f e c t i v e l y removed any s t r o n g near-s u r f a c e v e r t i c a l s t r u c t u r e and enhanced mixing g e n e r a l l y h e l p i n g to c r e a t e t h i s c h l o r o p h y l l f i e l d . However i f the source of va r i a n c e between 20 and 90m i s an i n t e r n a l wave e f f e c t or due to v e r t i c a l shear and g r a d i e n t s , then t h e r e must be v e r t i c a l s t r u c t u r e below the near s u r f a c e r e g i o n . v Georgia S t r a i t 1,3,5m - J u l y F i n a l l y l e t us examine some Georgia S t r a i t data frcm the month c f J u l y . Apart from the oxygen spectrum of the 5 m data, the r e s u l t s are s i m i l a r to those a l r e a d y presented and are 105 S Q U A M I S H f i g . 37: Geographical p l o t of c h l o r o p h y l l b l o c k averages f o r Howe Sound lm data. 106 S Q U A M I S H f i g . 38: Geographical p l o t of s a l i n i t y b l o c k averages f o r Howe Sound lm data. 107 presented only f o r completeness ( f i g u r e s 39-44). None of the sp e c t r a presented i n t h i s s e c t i o n have been c a l c u l a t e d from detrended data. The oxygen spectrum (GS 5m) however deserves some d i s c u s s i o n . Again the t o t a l v a r i a n c e given i n t a b l e I shows that s i g n a l c o n d i t i o n s are not good and so the noise l e v e l i s reached f a i r l y r a p i d l y . Then the spectrum climbs s i n c e a white noise spectrum has a +1 s l o p e when p l o t t e d logfl;-leg -?' and f i n a l l y turns f l a t when the f i l t e r begins to take e f f e c t . I f there i s n ' t any s m a l l s c a l e a c t i v i t y i n the o r i g n a l d a t a , then t h i s occurence i s l i k e l y . These Georgia S t r a i t data are important because cf the la r g e s c a l e s p a t i a l d i s t r i b u t i o n s of c h l o r o p h y l l which are dep i c t e d i n f i g u r e 45. As the s a l i n i t y i n c r e a s e s as we remove o u r s e l v e s from the i n f l u e n c e of the F r a s e r R i v e r , higher c h l a. values are encountered. T h i s o b s e r v a t i o n i s i n agreement with data cf Parsons et a l (1970) and what i s p r e d i c t e d by some models (de Lange Boom, 1976). I t might show the l a r g e s c a l e a d v e c t i v e e f f e c t s c f the F r a s e r B i v e r , b u i l d i n g up a c h l o r o p h y l l maximum at the edge of i t s plume. However these r e s u l t s can a l s o be e x p l a i n e d b i o l o g i c a l l y as w e l l . The r i v e r - f o r c e d regime i s r e l a t i v e l y f r e e c f n u t r i e n t s compared to the surrounding Georgia S t r a i t waters and so b i o l o g i c a l growth might be l i m i t e d w i t h i n the b r a c k i s h waters of the plume. The r i s e i n c h l o r o p h y l l values at the edge of the plume would then net be a p h y s i c a l p i l i n g up of phytoplankton but r a t h e r an e x h i b i t i o n cf the d i f f e r e n t growth environments i n Georgia S t r a i t . The l o c a t i o n of t h i s maximum or at l e a s t of the t r a n s i t i o n from lower to higher c h l o r o p h y l l values i s l i k e l y to change depending G.S. 1 JULY f i g . 39: Spectra f o r J u l y , Georgia S t r a i t data taken at a depth of lm. 0 8 1 J U L Y g. 40: Coherences f o r the J u l y , Georgia S t r a i t , lm data. LLt G.S.5 JULY CI f i g . 43: Spectra f o r the J u l y , Georgia S t r a i t , 5m data. £11 114 on the s t a t e of the t i d e and the s t r e n g t h and d i r e c t i o n of the wind f i e l d s i n c e both of these f a c t o r s a f f e c t the shape of the plume. 115 GEORGIA ST. - JULY « o - i C H L . a. mg./m: I m. s o o tt-o SALINITY 546 m. f i g . 45: P l o t s of block averages f o r the J u l y Georgia S t r a i t data. To move to the r i g h t i s to move away from the mouth of the Fraser r i v e r . 116 4.5 Averaging We are i n t e r e s t e d i n o b t a i n i n g an overview, some g e n e r a l i t y c o n cerning the aspects of p h y s i c a l - b i o l o g i c a l i n t e r a c t i o n s , but t h i s i s more d i f f i c u l t . Most of the i n t a c t data r e c o r d s are of s h o r t d u r a t i o n , 25 minutes or so, and from such data i t i s d i f f i c u l t t o assess the nature of the parameter f i e l d s at very l a r g e s c a l e s s i n c e the s t a t i s t i c s are not based on a l a r g e enough sample t o give s a t i s f a c t o r y r e s u l t s i n the low f r e q u e n c i e s . Moreover i n a r r i v i n g at an 'average* r e s u l t , we are faced with the r a t h e r obvious b i a s e s i n h e r e n t i n the analysed data: that i t was not obtained i n e g u a l q u a n t i t i e s i n a l l l o c a t i o n s and at the same time so t h a t f o r example more of the 1 m r e s u l t s might have been ob t a i n e d i n Howe Sound than i n other study a r e a s , or more o f the data might have been obtained i n J u l y r a t h e r than other months. Also i f one wishes to average a l l the data t o g e t h e r , how i s i t to be accomplished? Do we assume each data run i s a separate e n t i t y , an i n d i v i d u a l process, and average the r e s u l t s l i n e a r l y or do we assume each r e c o r d i s a measure of the same process which should be s t a t i s t i c a l l y s t a b l e , and average the s p e c t r a l e s timates before c a l c u l a t i n g coherences and s p e c t r a ? Each method weights the r e s u l t s d i f f e r e n t l y because of the i n e q u a l i t i e s i n the length of record o b t a i n e d and the v a r i a b i l i t y i n the a c t u a l data. However i f one b e l i e v e s there i s some s i m i l a r i t y of s t r u c t u r e then i t should be p o s s i b l e to o b t a i n some meaningful averages i n the sense t h a t one can p r e d i c t the outcome of f u r t h e r s i m i l a r measurements w i t h i n s t a t i s t i c a l l i m i t s . 117 For example f i g u r e 46 i s a p l o t of temperature and s a l t coherences with c h l o r o p h y l l f o r the month of J u l y , where the es t i m a t e s have been p l o t t e d r e g a r d l e s s of l o c a t i o n or the depth of sampling. There are ten runs d i s p l a y e d and the s i g n i f i c a n c e l e v e l i s the l i n e a r average of a l l ten s i g n i f i c a n c e l e v e l s . There i s one obvious f e a t u r e present i n the p l o t , and t h a t i s the d i p i n coherence at about the 10 m s c a l e s i z e . T h i s seems to be a common f e a t u r e of a l l coherences i n v o l v i n g c h l o r o p h y l l but i s more e m p h a t i c a l l y present i n the J u l y data than i n other months, as has been d i s c u s s e d p r e v i o u s l y . Perhaps a good d e s c r i p t i o n of the r e s u l t s , i s t h a t t h e r e are l a r g e v a r i a t i o n s from data run t o data run but i t i s a l s o c l e a r t h a t t h e r e i s a measureable r e l a t i o n s h i p on average. One might average the coherences and phases l i n e a r l y to o b t a i n an average r e s u l t . Averaging the coherence, which i s a p o s i t i v e d e f i n i t e g u a n t i t y , i s a meaningful t h i n g to do as i t g i v e s an estimate of what to expect. The v a r i a b i l i t y i n the i n d i v i d u a l data w i l l be expressed i n the e r r o r bars which would be comparable to those of i n d i v i d u a l data runs shown e a r l i e r although the theory of Chapter I I I would p r e d i c t s m a l l e r v a l u e s because of the i n c r e a s e d number o f degrees of freedom i n each e s t i m a t e . The 95% s i g n i f i c a n c e l e v e l would drop a l s o because of the i n c r e a s e d number of degrees of freedom. However a l i n e a r average of the phases shown i n f i g 46, which would be around 90° , would not be r e p r e s e n t a t i v e o f the o r i g i n a l data which was e i t h e r 0° or 180°. T h i s f a c t suggests that the phases should be f o r c e d to e i t h e r 0° or 180* before averaging and although t h i s method w i l l hide the e x i s t e n c e of 118 o ~ ° . a ' UJ CO OC X 0 _ a CD *—* I *• * 7 3.0 2.0 l.O 0 0 LOG DISTANCE (M) o UJ C_> UJ X o o a a ' O ><o a UJ CO cc X 0_o CO —i _ I • • * 4 • 4 • • • • • • • • / • • • • • * 3.0 2.0 1.0 0.0 LOG DISTANCE (M) i -1.0 -2.4J 3-0 2-0 1.0 0.0 -1 0 : 1 1 I I -2.0 SRLT-CHL R T- ,• ^ 7 W P T O r -1.0 -2.fl f i g . 46: C h l o r o p h y l l coherences w i t h temperature and s a l i n i t y f o r 10 runs i n J u l y p l o t t e d regardless of sampling depth or l o c a t i o n , or number of blocks i n the run. 119 one phase r e l a t i o n s h i p the e r r o r bars w i l l demonstrate the v a r i a b i l i t y i n the data. I f we wish to o b t a i n some i n f o r m a t i o n concerning the phase and coherence i n the SCOS-low range, then i t i s necessary to average i n a d i f f e r e n t manner. Since the SCOB-low es t i m a t e s from i n d i v i d u a l data runs have only 2 degrees of freedom i n each or the f i r s t 4 e s t i m a t e s , t h e i r value w i l l always be 1.0 and hence a l i n e a r average o f them w i l l a l s o be 1.0. But s i n c e we are averaging a number of runs together we can t r e a t the SCCH-low s t a t i s t i c s as an ensemble and compute average g u a n t i t i e s of CO and QUAD before c a l c u l a t i n g coherences. Because the number of degrees of freedom i s i n c r e a s e d the values obtained w i l l not be i d e n t i c a l l y 1.0. In order to c a l c u l a t e average ' CC and QUAD i t i s f i r s t necessary to normalize the c o s p e c t r a l e s t i m a t e s from each i n d i v i d u a l run using the area under the cospectrum so that no bi a s w i l l be i n t r o d u c e d i n t o the average because of i n c r e a s e d c o v a r i a n c e i n one p a r t i c u l a r run. Averaging these normalized g u a n t i t i e s i s p o s s i b l e provided one takes care of the phase problem. Averaging runs with 0° phase with those of 180° phase w i l l cause a lower value of average CO s i n c e the CO has d i f f e r e n t s i g n s f o r these values of phase. T h i s c a n c e l l a t i o n of CO w i l l cause a lower value of coherence than might be expected. T h e r e f o r e with t h i s method of averaging i t i s necessary t c f o r c e the phase to 0 or 180 . The averages of normalized power s p e c t r a are shown i n f i g s 47-49. They have been averaged i n frequency space and p l o t t e d a g a i n s t a d i s t a n c e s c a l e c a l c u l a t e d assuming d i s t a n c e = c / f where c = 1.0 ra/sec. The co n f i d e n c e 120 i n t e r v a l f o r each estimate i s 68$ and was c a l c u l a t e d from the v a r i a b i l i t y i n the data. Seven long data runs, most of which have been d i s c u s s e d i n the pr e v i o u s s e c t i o n , were averaged to produce these r e s u l t s . They are those l i s t e d i n Table I with 10 or more blocks of except run GS-5 f o r J u l y . The temperature s p e c t r a show the expected s i m i l a r i t y with some evidence of the smoothing a c t i o n of the pump's mixing showing up i n the decreased s p e c t r a l amplitude of the v a r i a n c e a s s o c i a t e d with s h i p motion (about l o g d i s t a n c e = 0.8), and i n the s l i g h t l y s t e e p e r r o l l - o f f beyond about l o g d i s t = 1.3 i n the inboard TEMP spectrum. The s p e c t r a maintain the red aspect of the i n d i v i d u a l s p e c t r a and perhaps have a h i n t of a source of var i a n c e around l o g d i s t = 1.3 - 1.5, which i s more n o t i c e a b l e i n the TOOT spectrum. The sl o p e of the cascade from the SCCE-low r e s u l t s to l o g d i s t = 1.5 or so i s about 0.5 and i s s i m i l a r t o a Kolmogoroff s l o p e o f -2/3 (Hinze, 1959). The s a l i n i t y spectrum shows f e a t u r e s s i m i l a r t o those of the temperature s p e c t r a . The r o l l - o f f from about l o g d i s t = 1.2 - 1.3 i s not as steep as t h a t o f TEMP probably because of b e t t e r instrument response and perhaps i n d i a c a t i n g t hat the r o l l - o f f i n the inboard temperature spectrum i s not a l l due to pump mixing but a l s o t h e r m i s t o r response which might not be as good as expected. Again the slope at l a r g e r s c a l e s i s about 0.5. C h l o r o p h y l l shows a s l i g h t y smoother spectrum at the s m a l l e r s c a l e s p a r t i a l l y because of instrument response and a l s o because the v a r i a n c e due to s h i p motion was not present i n the o r i g i n a l data. The shape of the spectrum i s s i m i l a r to the other s p e c t r a i n c l u d i n g the 0.5 r o l l o f f a t l a r g e r s c a l e s and the 121 RVERflGES a a f i g . 48: Average sa l i n i t y and chlorophyll spectra for the longer data runs. AVERAGES 1 2 4 i m p l i e d source o f va r i a n c e at l o g d i s t a n c e = 1.5. The average oxygen spectrum was c a l c u l a t e d from detrended data and i s i n d i c a t i v e of the poor response c h a r a c t e r i s t i c s of the probe although down to about l o g d i s t a n c e = 2.0 i t i s s i m i l a r t o the other s p e c t r a . The coherence and phase s p e c t r a were obtained i n the f o l l o w i n g manner. The phase was adjus t e d to be around 0 by m u l t i p l y i n g the normalized CO and QUAD- s p e c t r a l q u a n t i t i e s by -1 where necessary. For the SCOB-low est i m a t e s the i n d i v i d u a l CO and QUAD estimates were averaged t o o b t a i n average CO and QOAD and the coherence and phase c a l c u l a t e d using these mean q u a n t i t i e s . The remaining values of coherence and phase are l i n e a r averages o f the coherences and phases ( a f t e r f o r c i n g the phases near 180* t o be near zero) of i n d i v i d u a l data r u n s . The confidence bands on the r e g u l a r SCOB es t i m a t e s are 95% l i m i t s based on the observed v a r i a b i l i t y i n the da t a . The s i g n i f i c a n c e l e v e l was c a l c u l a t e d i n the same manner as those l e v e l s of oth e r coherence p l o t s . I t i s encouraging that the coherence s p e c t r a f o r the s m a l l e r s c a l e s which are l i n e a r averages are almost i d e n t i c a l to those c a l c u l a t e d using by f i r s t f i n d i n g average CO and QUAD values which means th a t the r e s u l t s are meaningful s i n c e the s t a b i l t y i n the s t a t i s t i c a l r e s u l t s i n d i c a t e s t h a t they are not a r t i f a c t s of the method used t o o b t a i n them. One should probably not read very much i n t o the SCOR-low r e s u l t s s i n c e there are p e c u l i a r phasing problems f o r some of these estimates and they are based on a l i m i t e d number of samples; but one would hope t h a t the 14 degrees of freedom i n 125 these estimates i s adeguate so t h a t the r e s u l t s say something about the data. Also the very s m a l l s c a l e r e s u l t s s h c u l d be ig n o r e d as d i s c u s s e d above. I t i s a l s o encouraging t h a t the co n f i d e n c e bands f o r coherence and f o r the power s p e c t r a are very s i m i l a r t o those of i n d i v i d u a l data runs although those c a l c u l a t e d by the formula of Chapter I I I w i l l g i v e s m a l l e r bands a t the s m a l l e r s c a l e s because of the i n c r e a s e d number of degrees of freedom. The average coherences are s i m i l a r t o those of i n d i v i d u a l runs al r e a d y d i s c u s s e d ; as we might expect the values are g e n e r a l l y higher at the l a r g e r s c a l e s , except i n the SCOB-low range f o r soite parameters, and then decrease as the s m a l l e r s c a l e s are reached. The r e s u l t s at the very s m a l l s c a l e s (< log d i s t a n c e = 0.5) are u n r e l i a b l e as d i s c u s s e d p r e v i o u s l y . Both temperature and s a l i n i t y seem f a i r l y w e l l r e l a t e d with c h l o r o p h y l l at about the 0.5 l e v e l of coherence at the l a r g e r s c a l e s with the SALT-CHL A coherence m a i n t a i n i n g t h i s l e v e l out to about l o g d i s t a n c e = 1.2. T h i s s c a l e i s a s s o c i a t e d with the •knee* i n the s a l i n i t y and c h l o r o p h y l l average s p e c t r a and the drop i n coherence might i n d i c a t e t h a t the sources of v a r i a n c e f o r the parameters a t t h i s s c a l e s i z e are u n r e l a t e d or that perhaps there i s some c a n c e l l a t i o n of CO because of phase d i f f e r e n c e s . T h i s drop i n coherence i s a s s o c i a t e d with a s h i f t i n the average phase towards 90* f o r t h i s s c a l e i n d i c a t i n g v a r i a b i l i t y i n the i n d i v i d u a l run phase e s t i m a t e s t h a t went i n t o the averaging. The SCOB-low r e s u l t s f o r both TEMP-CHL A and SALT-CHL A are f a i r l y h i g h , about 0.6, and are not a l l s i g n i f i c a n t although one ,4.0 4.0 3 -° . 2-0 l.O iTo LOG DISTANCE IMJ -2.0 1.0 4.0 T 3.0 1 2.0 - r — r LOG DISTANCE' (M) °"° -1.0 f i g . 50: Average chl. a coherences with temperature and salinity based on 7 of the longer data runs. See the text tor details concerning the calculations. PHASE (X10] J COHERENCE -J8.0 0.0 L8.0 0.0 0.5 I. Q CD M 2 ° C O — I •JO z o n \ -^b 3 i — e — ^ i —e— i i — e — i i—9—I H—9—I i — e — i r-e-H i — - e — i PHASE (X10J ) -18.D 0.0 1B.0 ui u a CD M W b O b C D — I D O rT'-. b ^_b 3 i e 1 H3H i — e — i i e 1 r-e-i y& van r-€H e COHERENCE 0.0 0.5 1.1 i i I 1 1 i 1 1 I 1 1 I 1 1 t — i — i O CD ro 2 ° co —i 3D Z O m _ „ PHASE (XIOL J COHERENCE 1B.0 0 J 1B.0 0.0 0.5 I. J . L i e 1 i — e — i h-en i — e — i i-e-i i — e — i r-6H I O I r-en i — e — i hen h-e-H if1 ~i r I U) u a CD ro ro b 2 ° C O D CD i i „ PHASE (XI0J ) COHERENCE 1B.0 0.0 1B.0 0.0 0.5 1 0 J 1 . I I I B 1 I—S—I i — e — i i-e-t i — e — i i — e — i I-6H i-en r-6H r-en i-en i-eH KM •ief-1 - i ' r 128 would l i k e t o b e l i e v e t h a t with 14 degrees of freedom, these coherences do have some meaning. The f i r s t e s t i m a t e i n the SALT-CHL A coherence spectrum i s q u i t e low and might be caused by v a r i a b i l i t y i n the phases of the i n d i v i d u a l e stimates which i s i n d i c a t e d by the width of the c o n f i d e n c e band f o r the phase of t h a t e stimate. Oxygen appears f a i r l y w e l l r e l a t e d t o c h l o r o p h y l l between l o g d i s t = 3 and l o g d i s t = 1 .5 but drops o f f at the s m a l l e r s c a l e s and a l s o i n the SCOR-lcw range. The phase does not seem to be a problem f o r these l a r g e s c a l e e s t i m a t e s and so perhaps the low SCCfi-lcw coherences are r e a l . Temperature shows coherences with oxygen t h a t are s i m i l a r to those of oxygen and c h l o r o p h y l l except that the TEHP-02 r e s u l t s show a h i n t of an i n c r e a s e around the s c a l e a s s o c i a t e d with ship motion as does the s a l i n i t y - o x y g e n coherence. For both TEMP-02 and SALT-02, the SCCB-low phases have wide confidence bands and coherences mainly below the s i g n i f i c a n c e l e v e l . Temperature and s a l i n i t y are r e l a t e d at about the 0.6 l e v e l down to s c a l e s of about l o g d i s t a n c e =0.8 although i n the SCCB-low range they do not appear t o be s i g n i f i c a n t l y r e l a t e d . The phase estimates f o r these SCCB-low s c a l e s show l a r g e e r r o r bars i n d i c a t i n g an unsteady phase r e l a t i o n s h i p which might p c s s i b l y a f f e c t the coherence r e s u l t s f o r those s c a l e s . The o v e r a l l impression obtained from these averages of s p e c t r a i s t h a t there appears to be a f a i r l y c l o s e a s s o c i a t i o n between the p h y s i c a l and b i o l o g i c a l worlds e s p e c i a l l y a t l o n g e r s c a l e s apart from the SCOB-low range. The coherences are q u i t e high (> 0.5) f o r s c a l e s g r e a t e r than 10m and the power s p e c t r a 129 show s i m i l a r i t i e s i n shape i n the r e g i o n s of in p u t t o v a r i a n c e . Although the SCOR-low r e s u l t s might not he c l e a r c u t and perhaps are not i n d i c a t i v e of the t r u e nature of the r e l a t i o n s h i p s i n a l l i n s t a n c e s both temperature and s a l i n i t y have c o n s i s t e n t l y high coherences with c h l o r o p h y l l i n the SCOR-low s c a l e s . Note t h a t we have f o r c e d the phase t o 0° when i t i s near o 180 as we have seen the phase i n an i n d i v i d u a l data run lay be near 0° (in phase) or near 180° (cut of phase). 130 CHAPTEB V CONCLUSIONS Before any of the r e s u l t s , the measuring procedure w i l l be d i s c u s s e d s i n c e one c f the purposes of the study was t c examine measurement technigue and there were some problems with the methods used here. f o r example, i n s i t u f l u c r o m e t r y i s a mere a t t r a c t i v e a l t e r n a t i v e to that used i n these experiments because the pumping system does smooth the s m a l l e r s c a l e v a r i a t i o n s . However most of the v a r i a t i o n i s at l a r g e s c a l e s so f o r mapping down t c s c a l e s of a few tens of meters the present system w i l l work. Nor i s a f i x e d r i g i d bcom attached to a s h i p the best sampling p l a t f o r m because of i t s s e n s t i v i t y to wave motion. However f l u o r c m e t r y does appear to be a reasonable method of o b t a i n i n g l a r g e amounts of i n f o r m a t i o n about a phytoplankton f i e l d . I t would a l s o be d e s i r a b l e to sample i n such a manner that c o n t o u r i n g or mapping of the c h l o r o p h y l l d i s t r i b u t i o n i s p r a c t i c a l although t h i s i s not always p o s s i b l e s i n c e i t i s s u b j e c t t o c o n s t r a i n t s such as the s i z e of v e s s e l used and the dimensions of the area cf i n t e r e s t . A l s o , i f one i s to g e o g r a p h i c a l l y map the biomass then one probably should depth average the r e s u l t s to remove the e f f e c t s caused by the v e r t i c a l g r a d i e n t of the c h l o r o p h y l l d i s t r i b u t i o n and the i n t e r a c t i o n s with wave f i e l d s e i t h e r s u r f a c e or i n t e r n a l . C l e a r l y one wants to be able to move f a s t e r and to c y c l e the pump i n t a k e up and 131 down f a i r l y r a p i d l y as one moves. The peak t o peak v a r i a t i o n s i n the c h l o r o p h y l l d i s t r i b u t i o n s measured were u s u a l l y l e s s than 50% of the mean value so that i t was not o f t e n t h a t a d i s c r e t e sample wculd show a exaggerated d i f f e r e n c e from one taken a short d i s t a n c e away, when the block averages are examined i t i s found t h a t the v a r i a b i l i t y over d i s t a n c e s of about 250 m i s l e s s than 20$ of the mean and u s u a l l y i s on the order of 10%, T h i s i n f o r m a t i o n i s of use when design i n g d i s c r e t e sampling programs. S p e c t r a l a n a l y s i s of the data r e v e a l e d t h a t the c o n t r i b u t i o n s tc the variance i n the c h l o r o p h y l l f i e l d as viell as those of the ether parameters i s mainly at l a r g e r s c a l e s although o c c a s i o n a l l y there are other sources at s m a l l e r s c a l e s . The s p e c t r a are u s u a l l y s i m i l a r i n shape and t h i s lends credence t o the hypothesis t h a t the sources of v a r i a n c e f o r the d i f f e r e n t parameters are s i m i l a r . T h i s i s f u r t h e r s u b s t a n t i a t e d by the r e s u l t s c f coherence a n a l y s i s as u s u a l l y at the l a r g e r s c a l e s the coherence i s g r e a t e r than 0.5. Although there were s i t u a t i o n s encountered when t h i s was not the case, the average r e s u l t s i n d i c a t e that f a i r l y s t r o n g r e l a t i o n s h i p s e x i s t . A dominant p h y s i c a l f o r c e i n the i n l e t s and i n the r e g i o n of Georgia S t r a i t where measurements were taken i s the i n f l o w cf f r e s h water. Some of the energy a v a i l a b l e f o r mixing w i l l come from t h i s source although i n the near surface r e g i o n the wind and wave a c t i o n w i l l a l s o play a r o l e . Some of the v a r i a n c e measured at the l a r g e r s c a l e s i s a l s o the r e s u l t cf d i f f e r e n t p h y s i c a l and b i o l o g i c a l regimes caused by a l a c k of mixing. For example i n the Georgia S t r a i t data there i s l i k e l y t c be l a r g e 132 s c a l e d i f f e r e n c e s because of the nature of the r i v e r water. The b r a c k i s h water i s n u t r i e n t d e f i c i e n t compared to the surrounding waters and probably cannot support as great a phytoplankton crop. Also near the head of i n l e t s such as Howe Sound, seme of the v a r i a n c e encountered w i l l be a r e s u l t of the f a c t t h a t the r i v e r maintains i t s i n t e g r i t y f o r a c o n s i d e r a b l e d i s t a n c e from the head. Tracks across the r i v e r w i l l show v a r i a b i l i t y because of t h i s e f f e c t (H-1 dat a ) . St s m a l l e r s c a l e s the r e l a t i o n s h i p s netween parameters are o f t e n going to depend on the v e r t i c a l d i s t r i b u t i o n s i n t e r a c t i n g with the p h y s i c a l processes c f v e r t i c a l mixing as was d i s c u s s e d i n the Indian Arm 5m data of June. Very o f t e n i n the s p e c t r a there are sources of v a r i a n c e at the s n a l l e r s c a l e s , l e s s than 100m or so, and these might be a t t r i b u t e d to i n t e r n a l wave e f f e c t s cr s h i p n o t i o n . Beyond these s c a l e s the s l o p e s of the r o l l - o f f of l o g f $ are u s u a l l y between -1 and -2. I f we remove the f i l t e r i n g e f f e c t s of the pumping system which we b e l i e v e steepens the slope by abcut -1 near s c a l e s of 10m, then i t i s usual to f i n d s l o p e s of l o g f j . vs l o g f of between 0 and -1 which corresponds to r e s u l t s of other observers (eg Benman and P i a t t , 1974). when d e s i g n i n g a sampling program one should be aware of the d i f f i c u l t i e s of o b t a i n i n g r e l i a b l e r e s u l t s p a r t i c u l a r l y i f the s a n p l i n g i s to be done d i s c r e t e l y s i n c e t h i s type of sampling near the head of an i n l e t or near the bcrder of a r i v e r plume might p e s s i b l y l e a d to misconceptions regarding the nature of the parameter f i e l d . However f o r most b i o l o g i c a l purposes a c a r e f u l l y planned d i s c r e t e sampling program should s u f f i c e and the added e f f o r t of continuous measurement i s not necessary. F i n a l l y there appears 133 to be a f a i r l y i n t i m a t e r e l a t i o n s h i p between the b i o l o g i c a l and the p h y s i c a l worlds most of the time, e s p e c i a l l y at l a r g e r s c a l e s and t u r b u l e n t mixing processes do appear to a f f e c t the d i s t r i b u t i o n of phytoplankton , 134 APPENDIX A BCT WEDGE BESOITS Because there were problems i n v o l v i n g the o p e r a t i o n c f the hot wedge v e l o c i t y sensor, i t was decided not to i n c l u d e the r e s u l t s i n the main t e x t . The s i g n a l from the prcbe was g e n e r a l l y very noisy and would seem to "knock-out" or s h i f t i t s o f f s e t very s l i g h t l y o c c a s i o n a l l y . One probe t h a t became i n o p e r a t i v e showed nothing mechanically wrong when s u p e r f i c i a l l y i n s p e c t e d , but perhaps there was a m i c r o - s p l i t i n the p r o t e c t i v e quartz c o a t i n g . One c e r t a i n i n d i c a t i o n of a f a u l t y prcbe was the l a r g e i n c r e a s e i n c u r r e n t drawn by the probe, almost as i f i t were pumping the power i n t o the ocean. Another common problem was the f l o o d i n g of the connector between the prcbe and the prcbe holder even though care was taken when s e a l i n g i t up. Most of the hot wedge data were of l i t t l e use, but here we w i l l present seme c f the b e t t e r r e s u l t s . F i g u r e 52 i s the spectrum f c r the wedge f o r seme In d i a n Arm, 3 m, data taken i n A p r i l . There appears to be a source of vari a n c e around 150 to or so followed by a cascade with slope s i m i l a r to Kolmogoroff (-2/3, Hinze, 1959) s l o p e and then steepening around 10 m. The outboard t h e r m i s t o r spectrum shows a s i m i l a r i t y i n shape and the coherence between the two parameters ( f i g u r e 53) i s g u i t e high i n d i c a t i n g a strong r e l a t i o n s h i p , thereby r e i n f o r c i n g the c o n t e n t i o n that 135 temperature can be used as a t r a c e r f o r the t u r b u l e n t v e l o c i t y f i e l d . Coherence p l c t s with c h l o r o p h y l l and s a l i n i t y show weaker r e l a t i o n s h i p s except i n the mid band range or the wedge-s a l i n i t y p l o t . The s a l i n i t y spectrum ( f i g 52) i s f l a t at the l a r g e r s c a l e s and a l s o through the mid-band r e g i o n t c about 10m or so and then decreases r a p i d l y . The other s p e c t r a do net show t h i s d i s t r i b u t i o n of variance over such a wide range cf s c a l e s , p a r t i a l l y because cf response c h a r a c t e r i s t i c s , and i n t h i s r e s p e c t the s a l i n i t y spectrum i s anomalous. Another wedge spectrum ( f i g u r e 54), t h i s one from some Indian Arm 5 m data, shews a very poor s i g n a l to noise r a t i o and the very sm a l l s c a l e s show the nois e l e v e l s . The l a r g e r s c a l e s s t i l l have strong coherences ( f i g . 55) with temperature , l e s s strong with s a l i n i t y and b a r e l y s i g n i f i c a n t with c h l . a. I t would have been nice to have the spectrum of the h o r i z o n t a l v e l o c i t y f l u c t u a t i o n s but i t appears that o p e r a t i o n of the prcbe i s n o n - t r i v i a l and r e q u i r e s more e f f o r t than could be put i n t o i t i n v i e s cf a l l the other instruments t h a t had to be operated at the sane time. I 3 o - r • q g. 52: S p e c t r a f o r some A p r i l I n d i a n Arm 3m dat a i n c l u d i n g the hot wedge, i-b TO ,? .o — C D - I UJ CO cr WW i 1 1 3-0 2.0 1.0 0.0 LOG DISTANCE (M) 2.0 -1.0 -2 .0 .3.0 UJ cj z C C Q ' U J X o o UJ cn (X x Q. 2.0 _1 1.0 _ J 0.0 _J dxfa <W>, «P -3.0 -2.0 WEDGE-SRLT I S — i 1 1 r 3.0 2.0 1.0 0.0 -1 .0 LOG DISTANCE (M) - 2 . « . 3 .0 UJ (_> z UJin 8-1 o UJ CO tr O O C3t J " c It >t >t JC 3c x mm -1.0 _I -2 .0 WEDGE-TOUT I 5 1 1 1 1 3.0 2.0 1.0 0.0 -1 .0 LOG DISTANCE (M) -2 .0 S i o •—4 UJ CO cr x 0_ d> d> f i g . 55: Hot wedge coherences f o r t h e A p r i l I n d i a n Arm 5m d a t a . -2.0 1 r 1 1— 3.0 2.0 1.0 0.0 -1 0 LOG DISTANCE (M) -2 .0 Co 140 APPENDIX E EUTE I MET DATA The data c o l l e c t e d from the f o u r t h sampling l o c a t i o n , Eute I n l e t , d i f f e r e d i n that they were obtained with the s h i p a t anchor r a t h e r than i n motion. T h i s allowed the c u r r e n t to advect the parameter f i e l d s past the pumping apparatus. Cne of the problems with t h i s method i s that the s h i p d i d not seem to a l i g n i t s e l f with the s u r f a c e c u r r e n t at a l l times, sc that perhaps the s h i p ' s h u l l s h e l t e r e d the boom sometimes. U n f o r t u n a t e l y t h i s p a r t i c u l a r t r i p was f r a u g h t with e l e c t r o n i c and r e c o r d i n g problems so t h a t very l i t t l e o f the data were usable. The r e s u l t s shown are based on data records of only 5 or 6 blocks. Not a l l the r e s u l t s are shown because of s p a t i a l l i m i t a t i o n s of t h i s t h e s i s , nor w i l l they be d i s c u s s e d a t great length s i n c e the d i s c u s s i o n would i n v o l v e a s i m i l a r treatment to that a l r e a d y given i n the chapter on r e s u l t s . F i g u r e 56 shows the c h l o r o p h y l l spectrum f o r seme Bute 1 m data. I t i s s i m i l a r to other c h l o r o p h y l l s p e c t r a already d i s c u s s e d except t h a t i t f a l l s o f f more r a p i d l y , with a steeper s l o p e . The two temperature s p e c t r a are notable because of t h e i r d i f f e r e n t appearances, the inboard t h e r m i s t o r shows l e s s variance around 2-5 m than the outboard t h e r m i s t o r . T h i s i s . much more e x p l i c i t i n some Eu 3 m data as shown i n f i g u r e 57, and i s probably the r e s u l t of the n i x i n g dene by the pump 141 i n t a k e . I t samples over a range of depth say 10 cm where the outboard t h e r m i s t o r measures at a p o i n t e s s e n t i a l l y . In a d d i t i o n to the l a r g e sampling range the water w i l l p r o b a b l y be drawn ever perhaps a 25 cm depth range . If the measuring i s t a k i n g p l a c e i n the t h e r m o c l i n e , the mixing dene by the pump i n t a k e s i l l p o s s i b l y and i s most l i k e l y to a f f e c t the s m a l l e r s c a l e s . When the s h i p i s i n motion the s t r e a m l i n e s of the pump a r e l i k e l y to be compressed mere towards the pump and so perhaps t h i s e f f e c t w i l l be n o t i c e d l e s s . F i g u r e 58 shew some coherence r e s u l t s with c h l o r o p h y l l and the two main p h y s i c a l p a r a m e t e r s . I t appears t h a t temperature and c h l o r o p h y l l were not very c o h e r e n t , but s a l i n i t y and c h l o r o p h y l l were. Indeed i n most of the Eute d a t a , s a l i n i t y and c h l o r o p h y l l are more c l o s e l y t i e d t o g e t h e r . Perhaps t h i s i s because , i n the upper l a y e r , temperature was more homogeneous than the other parameters . In g e n e r a l the Bute data resembled the e ther data t a k e n , the l a r g e s t d i f f e r e n c e s c c c u r i n g with the temperature s p e c t r a and the c h l o r o p h y l l spectrum b e i n g perhaps s t e e p e r i n the r o l l o f f than with the o t h e r d a t a . I t i s d i f f i c u l t to say i f t h i s i s a r e s u l t of the d i f f e r e n t s a m p l i n g methods. BUTE I f i g . 56: S p e c t r a f o r some May Bute lm d a t a . BUTE 3 -2.0 2.0 l.O 0.0 -1.0 O UJ a. to UJ o a 11?\ 1 T l ^ l 3 » — 1 1 1 — 0 2.0 1.0 0.0 LOG DISTANCE £MJ 3.0 ] I J T-OUT ITTTTX III1: f1J] IiK _ I \ I \ I i — i 1 1 1 1.0 0.0 LOG DISTANCE (M) -1.0 -2.0 T r 2.0 1.0 0.0 LOG DISTANCE (M) -1.0 -2.0 f i g . 57: Spectra f o r some May Bute 3m data. Note the shapes of the temperature spectra. CO H-CO • o 3 cn CD 00 O i 3 O O J |-l 03 O r t hj QI O • HD o o CD ^ CD 3 O CD CO r t nr r t CD 3 CD hj 0) r t C h* CD 01 3 C L CO QJ h-> H ' 3 H» O r t CD •3 C r t CD H 3 0) 3 CL, n A PHRSE IX101 ) COHERENCE 00 IB.O 36.0 0.0 0.5 1.0 o CD O e i i— e —I h6H I O I i — e — i > o < i — e — i , i — e — i i — e — i t—e—i i e 1 H — e 1 h e 1 3= El PHASE (X10J ) COHERENCE -IB.O 0.0 16.0 0.0 0.5 1 0 J 1 . I I -en -e-H I I Q Q I I h ^ PHASE (X101 o.o --.B.0" '36.0 0.0 COHERENCE _ PHASE .1X10' , - i 1 L ' O co co —i D o 0.0 18.0 COHERENCE 36.0 0.0 0.5 t.O J , C_ -e 1 — e 1 i e — i . i — — i i e-^H I B — - I 1 8 D P H R S E 0 l n X 1 0 1 ' , . „ „ „ COHERENCE -IB.O 0.0 IB.O 0.0 0.5 1 0 J — I . L _ I Cu 0! r t 01 0) CO t CD to —4 D i e~ i — e — i SSL i — e — i ^^  t=egL U) U l PHASE 1X10' ) COHERENCE -JB.0 0.0 18.0 0.0 0.5 1 0 1 1 . L. 5= cn —i u o i — e — i J # f i e 1 i e 1 he t7f7L 145 REFERENCES Bainbridge, Richard (1957). The s i z e , shape and density c f marine phytoplankton concentrations. B i o l o g i c a l Reviews 3 2(1) , pp. 91-115. Barnes, H. and S. M. Marshall (1951). On the v a r i a b i l i t y o f r e p l i c a t e samples and some applications of •contagious• series to the s t a t i s t i c a l d i s t r i b u t i o n of catches over-r e s t r i c t e d periods. Journal of the Marine Bioloq^cal Association 30, pp. 233-263. Bendat, Julius S. and Allan G. P i e r s o l (1971). Random Data: Analysis and Measurement Procedures. Wiley-interscienCP. Toronto. ~~ ~~' — Cassie, R. M. (1963). Microdistribution of plankton. Oceanography and Marine Bioloqy, (H. Barnes, ed.), 1, pp. 223-252. ~ Cook, James (1815). Captain Cook's Or i g i n a l Voyages Round The  World; Performed by Royal Authority. W, Smith and Co. , London. Darwin, Charles (1952). Journal of Researches into the Geology  and Natural History of the Various Countries Visited by  H.M.S. Beagle. Facisiraila reprxnt of the f i r s t e d i t i o n . Hafner Publishing Co., New York. Dentnan, K. and Trevor P i a t t (1974) . Coherences in the horizontal d i s t r i b u t i o n s of phytoplankton and temperature i n the upper ocean. Proceedings of the Sixth Colloquium on Ccean Hydrodynamics, Liege A p r i l 1974. de Lange Boom, B. (1976). Mathematical models of chlorophyll d i s t r i b u t i o n i n the Fraser r i v e r plume. M.Sc. thesis , In s t i t u t e of Oceanography, University of B r i t i s h Columbia, (in preparation). Garrett, John (1970). F i e l d observations of freguency domain s t a t i s t i c s and nonlinear e f f e c t s in wind-generated ocean waves. Ph.D. t h e s i s , I n s t i t u t e of Oceanography, University of E r i t i s h Columbia. Gilmartin, M. (1960)., The primary production of a B r i t i s h Columbia f j o r d . Ph.D. thesis. I n s t i t u t e of Oceanography, 146 University of B r i t i s h Columbia. Groves, G. and E. J. Hannan (1968). Time s e r i e s r e g r e s s i o n of s e a l e v e l on weather Reviews of Geophysics 6 (2), pp. 129-17 ty • -• Hardy, A. C. (1935). The continuous plankton r e c o r d e r . Discovery Reports 11_/ PP. 457-509. Herdman W. A. (1907). Plankton f i s h i n g o f f the I s l e of Mann. Report of the B r i t i s h A s s o c i a t i o n f o r the Advancement of Scien c e , pp. 550-553. Hinze, J . C. (1959). Turbulence. McGraw-Hill,New York. J e n k i n s , G. M. and D. G. Watts (1968). S p e c t r a l A n a l y s i s . Holden-Day, San F r a n c i s c o . K rauel, David P. (1972) . Cye d i f f u s i o n s t u d i e s i n the I r i s h Sea. Ph. D. t h e s i s . U n i v e r s i t y of L i v e r p o o l . L o f t u s , M. E., D. V. Subba Rao and H. H. S e l i g e r (1972). Growth and d i s s i p a t i o n of phytoplankton i n Chesapeake Bay, 1. Response to a l a r g e pulse of r a i n f a l l . Chesapeake Science 13(4), pp.282-299. Lorenzen, C. J. (1966). A method f o r the continuous measurement of an v i v o c h l o r o p h y l l c o n c e n t r a t i o n . Deep-Sea Research 13. pp. 223-227 — ' (1971). Continuity in the d i s t r i b u t i o n of surface chlorophyll. Journal du Conseil. 34(1), pp. 18-23. , C. E. (1941).Continuous plankton r e c o r d s : phytoplankton rn the North Sea 1938-39. Part I diatoms. H u l l B u l l e t i n of Marine Ecology 8, pp. 19-46. Macdonald, J.W. (1972). Fluxatron and sonic anemometer measurements of momentum flux at a height of 4 metres i n the atmospheric, boundary layer. M.Sc. thesis, Institu+o of Oceanography, University of B r i t i s h Columbia. National Oceanographic Instrumentation Center (1972). Ins* Fact Sheet IFS-733003. Washington B.C. 147 (1972). Instrumantion Fact Sheet IFS-73004. Washington D.C. Parsons, T. R., R. J. LeBrasseur and W. E. Barraclough (1970). Levels of production in the pelagic environment of the s t r a i t of Georgia, B r i t i s h Columbia: a review. Journal of the Fisheries Research Board of Canada 27 (7), pp. 1251-1263. Pia t t , Trevor (1972). Local phytoplankton abundance and turbulence. Deep-Sea Research 19(3), pp. 183-133. , and D. V. Subba Rao (1970). Energy flow and species d i v e r s i t y i n a marine phytoplankton bloom. Nature 227 (5262), pp. 1059-1060. "* L« H- Dicke and R. w. T r i t e s (1970). Spatial heterogeneity of phytoplankton in a near-shore environment. Journal of the Fisheries Research Board of Canada 27, pp. 1453-1*173. — P P Steele, John H. (1974). Spatial heterogeneity and population s t a b i l i t y . Nature 248, p. 33. Strickland, J. D. H. (1968). Continuous measurement of in vivc chlorophyll; a precautionary note. Deep-Sea Research 15, pp. 225-227. ~ and T. R. Parsons (1972). A P r a c t i c a l Handbook of Sea-water Analysis. Fisheries Research Board of Canada B u l l e t i n 167 (2nd ed.). U. S. Naval Oceanographic Office (1966). Handbook of  Oceanographic Tables. Washington D. C. Yentsch, C. S. and D. Menzel (1963). A method for the determination of phytoplankton chlorophyll and phaeophytin by fluorescence. Deep-Sea Research 10_, pp. 221-231. 

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