UBC Theses and Dissertations

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UBC Theses and Dissertations

Prototype of a continental shelf tide gauge Galloway, James Lewis 1974

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PROTOTYPE OF A CONTINENTAL SHELF TIDE GAUGE by JAMES LEWIS GALLOWAY B . A . S c , U n i v e r s i t y of B r i t i s h Co lumbia , 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In the Department of E l e c t r i c a l Eng ineer ing We accept t h i s t h e s i s as conforming to the requ i red standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1974 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 the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o lumbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e 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 purposes may be g r a n t e d by the Head o f my Department 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 not 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 . Department o f E l e c t r i c a l Eng ineer ing The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date 31 May 1974 i i ABSTRACT S p e c i f i c a t i o n s and design f o r a s e l f - c o n t a i n e d t i d e gauge are p resented . The gauge i s s u i t a b l e f o r immersion to a depth of 1000 meters f o r a per iod of one year wi th a f i v e minute sample r a t e . A V ib ro t ron absolute pressure t ransducer i s the sensing element with pressure measured to an e q u i v a l e n t water height of one m i l l i m e t e r . Instrumental and oceanic f i l t e r i n g of wind waves and t r a d e o f f s in sampling techniques are i n v e s t i g a t e d . Storage and reduct ion of data i s arranged to provide usefu l s t a t i s t i c a l i n f o r m a t i o n on instrument performance. Transducer c a l i b r a t i o n data a n a l y s i s i n d i c a t e s that c a r e f u l choice of c a l i b r a t i o n polynomial can s i g n i f i c a n t l y improve accuracy of t i d a l d a t a . In s i t u t e s t s and a n a l y s i s of r e s u l t s i n d i c a t e adequate instrument performance, but high p r e c i s i o n comparis ions between sea bottom pressure and measured water he ight are of l i m i t e d value i n the t e s t region due to v a r i a t i o n s in mean water d e n s i t y . Spectra r e s u l t s reveal the presence of se iches d i s t i n c t i v e to the t e s t r e g i o n . Comparisions between shore -based s t a f f readings and o f f s h o r e pressure data i n d i c a t e the p o s s i b l e presence of unusual dynamic water d e n s i t y s t r u c t u r e at the t e s t s i t e . i i i TABLE OF CONTENTS Chapter Page I INTRODUCTION 1 PREVIOUS WORK 3 II SPECIFICATIONS OF THE TIDE GAUGE 4 SPECIFICATIONS FROM A HYDROGRAPHIC POINT OF VIEW 4 Absolute Accuracy of Local Height of Tide . . 4 S t a b i l i t y of the Measurement 5 Sample Rate Requirements 6 Operat ing Depth Requirements. 7 I n s t a l l a t i o n Time Requirements 7 SPECIFICATIONS FROM AN IMPLEMENTATION POINT OF VIEW 7 Required R e s o l u t i o n of Pressure Measurements. 7 Corresponding Reso lu t ions Necessary f o r C o r r e c t i o n s to data 8 Transducer Requirements TO Time Base S t a b i l i t y 12 Recording System 13 I I I SAMPLING CONSIDERATIONS 15 TRADEOFFS TO CONSIDER IN SAMPLING TECHNIQUES. 15 The sampling C i r c u i t 16 Reso lv ing the Tradeoff Question 18 i v CONTENTS (cont inued) Chapter Page IV INVESTIGATION OF INSTRUMENTAL AND NATURAL DATA FILTERING 22 FILTERING EFFECT OF SIGNAL AVERAGING 22 NATURAL FILTERING IN THE OCEAN 25 F i l t e r i n g A c t i o n of Deep Water 25 A t t e n u a t i o n of Swell by Sea Ice . . . . . . . 26 V ELECTRONIC AND MECHANICAL DESIGN 28 ELECTRONIC DESIGN 28 MECHANICAL DESIGN 30 VI CALIBRATION PROCEDURES AND RESULTS 33 CALIBRATION PROCEDURE 33 ANALYSIS OF CALIBRATION DATA. . . » 34 Voltage and Temperature C a l i b r a t i o n s 35 A n a l y s i s of Pressure C a l i b r a t i o n Data 36 VII IN SITU TESTS AND DATA RECOVERY 40 PRACTICAL ASPECTS OF FIELD TESTS 40 Choosing a Test Region 40 I n s t a l l a t i o n and Recovery Techniques 41 OTHER FIELD TESTS RELATED TO THE TIDE GAUGE . . . 43 RECOVERY OF OFFSHORE TIDAL DATA 44 V CONTENTS (cont inued) Chapter Page VIII ANALYSIS OF TEST RESULTS 47 RESULTS OF HARMONIC ANALYSIS 50 LOW FREQUENCY PORTION OF THE POWER SPECTRUM . . 51 HIGH FREQUENCY PORTION OF THE POWER SPECTRUM. . 53 COMPARISON OF STAFF READINGS AND PRESSURE GAUGE READINGS 56 IX SUMMARY AND RECOMMENDATIONS 59 BIBLIOGRAPHY 62 APPENDIX 1 65 APPENDIX 2 71 vi LIST OF TABLES Table Page I C a l i b r a t i o n Constants f o r V ib ro t ron Transducers . 39 II D i f f e r e n c e Between Water Surface Leve ls and Pressure Gauge Readings 56 vi i LIST OF FIGURES Figure Page 2.1 Format of Data W r i t t e n on Tape 13 3.1 Bas ic Sampling C i r c u i t 16 4.1 A t tenuat ion of the Pressure E f f e c t of Surface Waves as Measured on the Sea F loor as a Funct ion of Frequency and Depth 26 4.2 Genera l i zed Amplitude Spectrum of Waves on the A r c t i c Ocean with the E f f e c t of Depth F i l t e r i n g inc luded 27 5.1 Exploded View of the Cont inenta l S h e l f Tide Gauge 32 6.1 Standard Dev ia t ion of C a l i b r a t i o n Data Verses C a l i b r a t i o n Curve Complexity 38 7.1 Typ ica l Tide Gauge I n s t a l l a t i o n fo r Howe Sound Test S e r i e s 42 8.1 Upper Howe Sound Showing Locat ion of Test S i t e . . 48 8.2 T i d a l Time S e r i e s Used f o r Data A n a l y s i s 49 8.3 Non-Averaged L ine Power Spectrum of S e r i e s H02 . . 52 8.4 F u l l Power Spectrum of S e r i e s H02 Featur ing Log-Band Averaging 55 8.5 Time S e r i e s of D i f f e r e n c e s between Water Surface Leve ls and Pressure Gauge Readings f o r S e r i e s H02 58 v i i i LIST OF VARIABLES V a r i a b l e D e f i n i t i o n a Constant in c a l i b r a t i o n equat ion b Constant in c a l i b r a t i o n equat ion c Constant in c a l i b r a t i o n equat ion d Constant in c a l i b r a t i o n equat ion e Constant in c a l i b r a t i o n equat ion f ( t ) Genera l i zed s i g n a l F Value of f requency , g e n e r a l i z e d spectrum g A c c e l e r a t i o n of g r a v i t y h Depth of ocean H Pressure t r a n s f e r f u n c t i o n j Square root of -1 k Integer v a r i a b l e , rad ian wave number m Integer v a r i a b l e n Integer v a r i a b l e p Pressure in N e w t 0 " s ( = P a , or Pasca l ) meter P Barometr ic Pressure o S^ S e n s i t i v i t y of depth re temperature ( = ^ ) t Time v a r i a b l e T Time i n t e r v a l , per iod i x LIST OF VARIABLES (cont inued) V a r i a b l e D e f i n i t i o n z Water height 6 Impulse f u n c t i o n £ Amplitude d i f f e r e n c e e Temperature v a r i a b l e X Wavelength p Mass d e n s i t y of water at Oceanographic d e n s i t y parameter T . Time i n t e r v a l 0)' Radian frequency X Time averaged value of x <x> Depth averaged value of x ACKNOWLEDGEMENT Merci to the P r o f e s s o r s , Graduate S tudents , and S t a f f of IOUBC who taught me the what, where, when, and why of water . D. Eng l i sh and H. Heckel of Oceanography cons t ruc ted mechanical po r t ions of the t i d e gauges. Mr. S. Wigen, T i d a l Super in tendent , MSD, prov ided thought fu l advice on t e s t r e s u l t s as we l l as s t a f f readings whi le on h o l i d a y s . Dr. J . MacDonald reviewed the e l e c t r o n i c design and suggested the format f o r reco rd ing data . S p e c i a l thanks to an e x c e l l e n t s u p e r v i s o r , Dr. T. Osborn, IOUBC, whose gent le encouragement and a s s i s t a n c e extended beyond the p r o f e s s i o n a l l e v e l . G ra t i tude t o , and a f f e c t i o n f o r , my c o - a u t h o r , c o - r e s e a c h e r , and w i f e , S h i r l e y , who stood by through good and bad. 1 Chapter I INTRODUCTION A c q u i s i t i o n of t i d a l data from c o n t i n e n t a l s h e l f regions over long per iods of time has been made f e a s i b l e by recent advances in the f i e l d of d i g i t a l e l e c t r o n i c s . The t ransducers and record ing systems requ i red by s e l f - c o n t a i n e d inst rument packages have been a v a i l a b l e f o r a number of years but , u n t i l the advent of complement ry -meta l -ox ide -semiconductor (CMOS) techno logy , i n s t a l l a t i o n s of longer than a few weeks were d i f f i c u l t and c o s t l y to implement. CMOS l o g i c , wi th i t s medium s c a l e i n t e g r a t i o n c a p i b i l i t i e s and i t s c h a r a c t e r i s t i c low power requirements has removed a t e c h n o l o g i c a l b a r r i e r from the sc ience of oceanography. Why measure t i d a l he ights on the c o n t i n e n t a l s h e l f at a l l ? Coastal i n s t a l l a t i o n s provide adequate data to p r e d i c t l o c a l t i d e s and the ins t rumenta l problems are f a r l e s s severe than those of o f f s h o r e i n s t a l l a t i o n s . Data from c o a s t a l i n s t a l l a t i o n s , however, i s i n f l u e n c e d by l o c a l geographic and m e t e o r o l o g i c a l c o n d i t i o n s and does not d e s c r i b e the progress ion of a t i d a l wave along the coast as we l l as data from an o f f s h o r e i n s t a l l a t i o n . T i d a l he ight data c o l l e c t e d on the s h e l f c o n t r i b u t e s to development of oceanic t i d a l models and a l so d e p i c t s the form of long per iod waves trapped by the c o n t i n e n t a l s h e l f . Mathematical modeling of coas ta l regions 2 can now prov ide accurate p r e d i c t i o n s of l o c a l t i d e s i f the models are given s u i t a b l e d r i v i n g f u n c t i o n s der i ved from o f f s h o r e d a t a . In A r c t i c regions i t i s d i f f i c u l t and, in some l o c a t i o n s , imposs ib le to measure t i d a l he ights from shore based s t a t i o n s dur ing the w in te r months because of the accumu-l a t i o n of l a r g e p ieces of i c e along the shore . In some respects an o f f s h o r e i n s t a l l a t i o n i n the A r c t i c i s i d e a l wi th regard to the data because in w in ter months the ex tens ive pack i ce f i l t e r s much of the wind generated wave energy so that l i t t l e a l i a s i n g o c c u r s . In summer months the l o w - l y i n g western A r c t i c i s s u s c e p t i b l e to storm surges and an o f f s h o r e t i d e gauge can provide d e t a i l e d i n f o r m a t i o n on b u i l d up and decay of a surge . The s p e c i f i c o b j e c t i v e of t h i s p r o j e c t may be s t a t e d as f o l l o w s : develop and t e s t a prototype of a c o n t i n e n t a l s h e l f t i d e gauge s u i t a b l e f o r long term i n s t a l l a t i o n s and perform a p r e l i m i n a r y a n a l y s i s of the t e s t r e s u l t s wi th a view towards determining e f f e c t i v e performance of the ins t rument . The design c o n s t r a i n t s are dependent upon a v a i l a b i l i t y of components and accuracy and s t a b i l i t y requirements of the data f o r hydrography purposes. Although the instrument i s designed f o r use on any c o n t i n e n t a l s h e l f , the s p e c i f i c a p p l i c a t i o n i s the A r c t i c Ocean. Two prototypes were a c t u a l l y cons t ruc ted as there i s always a p o s s i b i l i t y of l o s s of an instrument due to f l o o d i n g of the pressure housing or f a i l u r e to recover the package. 3 1.1 Prev i ous Work Much of the work in the f i e l d of o f f s h o r e t i d a l i n s t r u m e n t a t i o n has been concerned with s h o r t - t e r m deep-sea a p p l i c a t i o n s (see Snodgrass 1968, F i l l o u x 1970) . The importance of deep-sea t i d a l measurement has been emphasized by Munk and Z e t l e r (1967) . Long-term i n s t a l l a t i o n s on. the c o n t i n e n t a l shelf"* however, were not cons idered important u n t i l the recent expansion of s h i p p i n g a c t i v i t y in the Canadian A r c t i c and Hudson-James Bay r e g i o n s . In the p a s t , A r c t i c t i d a l data has been taken from shore-based s t a t i o n s p r i m a r i l y dur ing the summer with a l i m i t e d number of i n s t a l l a t i o n s o p e r a t i n g y e a r -round. Only a few hours of o f f s h o r e data has been c o l l e c t e d us ing sounding techniques from grounded i c e f l o e s (desc r ibed by Hunkins 1962) . 4 Chapter II SPECIFICATIONS OF THE TIDE GAUGE The design of an instrument i s guided and bounded by the s p e c i f i c a t i o n s p r e s c r i b e d by the end user of the d a t a - i n t h i s case the hydrographer. The des igner must then t r a n s l a t e the s p e c i f i c a t i o n s i n t o a form s u i t a b l e f o r implementat ion of the requ i rements . With t h i s in mind, both the hydrographic requirements and the f i n a l design s p e c i f i -c a t i o n s w i l l be d e s c r i b e d . 2.1 S p e c i f i c a t i o n s From a Hydrographic Po in t of View 2 . 1 . 1 Absolute Accuracy of Local Height of Tide Accuracy of the pressure measurement was s p e c i f i e d by the c o n t r a c t suppor t ing t h i s p r o j e c t to be e q u i v a l e n t to three cent imeters o f water he ight at t i d a l f r e q u e n c i e s . Accuracy of e x i s t i n g shore-based t i d e gauges i s near three cent imeters but t ransducers used f o r the o f f s h o r e gauge have a p o t e n t i a l f o r b e t t e r inherent accuracy than e x i s t i n g f a c i l i t i e s at d i u r n a l and h igher f requenc ies ( C a l d w e l l , Snodgrass, and Wimbush 1969) . G e n e r a l l y , the accuracy s p e c i f i c a t i o n should be determined by the geophys ica l background noise of the ocean. Even with a " p e r f e c t " p r e d i c t i o n of t i d a l he ight a v a i l a b l e , accuracy of the p r e d i c t i o n can be no b e t t e r than random noise 5 added to the ac tua l s i g n a l . The preceeding statement i s r e s -t r i c t e d to c o n d i t i o n s where data i s being c o l l e c t e d f o r purposes of p r e d i c t i n g t i d a l he ights v i a convent ional methods. P r e d i c t i o n i s d i s t i n c t l y d i f f e r e n t from a n a l y s i s where, in the l a t t e r c a s e , the noise l e v e l i t s e l f may be of i n t e r e s t (Munk and Car twr igh t 1966). The accuracy s p e c i f i c a t i o n may now be r e s t a t e d a s : accuracy of the data need be no b e t t e r than the geophys ica l s p e c t r a l no ise l e v e l . S ince the noise l e v e l of the ocean i s frequency dependent, the accuracy s p e c i f i c a t i o n i s a l s o a f u n c t i o n of f requency . As an approximate g u i d e l i n e noise l e v e l s near the coast at s e m i - d i u r n a l f requenc ies and lower are of the order of one cent imeter and decrease wi th i n c r e a s i n g frequency (based on t e s t r e s u l t s in Chapter V I I I ) . 2 . 1 . 2 S t a b i l i t y of the Measurement A s t a b i l i t y requirement i s a r e s t r i c t i o n on the net d r i f t of an i n s t r u m e n t ' s data* A net d r i f t added to t i d a l data w i l l i n f l u e n c e the very low frequency p o r t i o n of the spectrum most s t r o n g l y and t h i s i s compounded by the f a c t that t i d a l components at those f requenc ies are g e n e r a l l y s m a l l . The t ransducer used with the o f f s h o r e gauge e x h i b i t s a d r i f t that s i g n i f i c a n t l y contaminates very low frequency t i d a l components. For the purposes of hydrography a d r i f t rate of one m i l l i m e t e r per year i s a c c e p t a b l e . However, t h i s low d r i f t cannot be achieved by the o f f s h o r e gauge. The 6 e f f e c t i v e value of d r i f t i s determined in the s e c t i o n on data a n a l y s i s . 2 . 1 . 3 Sample Rate Requirements In the absence of n o n l i n e a r i t i e s and n o i s e , t i d a l data can be def ined with a sample i n t e r v a l of s i x hours . However, with the i n c l u s i o n of n o n l i n e a r i t i e s in the response of the ocean, which r e s u l t s in harmonics of the t i d a l components, and a d d i t i o n of the e v e r - p r e s e n t background n o i s e , the sample i n t e r v a l must be l e s s than s i x hours to a l low f o r dete rminat ion of the harmonics ( i n a Nyquist sense) and, of c o u r s e , to reduce the s t a t i s t i c a l e f f e c t of random n o i s e . With most shore based s t a t i o n s data i s logged on char t paper which i s l a t e r hand-d i g i t i z e d f o r a n a l y s i s so that labour costs e f f e c t i v e l y l i m i t the maximum sample r a t e . For the reasons d e s c r i b e d , hydrographers normal ly use a sample i n t e r v a l of one hour. With automatic data logg ing instruments i n c o r p o r a t i n g magnetic tape r e c o r d e r s , the p r i o r i t i e s are s h i f t e d so that the economy r e f e r r e d to above i s not s i g n i f i c a n t and i t becomes a quest ion of us ing a l l a v a i l a b l e storage in order to get a maximum amount of i n f o r m a t i o n from an i n s t a l l a t i o n . On t h i s bas is the sample i n t e r v a l was chosen to be s e l e c t a b l e at one of 0 . 6 2 5 , 1 . 2 5 , 2 . 5 , 5 . 0 , 10.0 minutes wi th an i n t e r v a l of f i v e minutes p r o v i d i n g one year of d a t a . 7 2.1.4 O p e r a t i n g D e p t h R e q u i r e m e n t s The t i d e g a uge d e s c r i b e d h e r e i s i n t e n d e d t o o p e r a t e on t h e c o n t i n e n t a l s h e l f , t h e l i m i t o f w h i c h a v e r a g e s t o 130 m e t e r s i n d e p t h . H o w e v e r , b e c a u s e an i m p o r t a n t l o c a t i o n t o m e a s u r e t i d e s i s on t h e c o n t i n e n t a l s l o p e w h i c h f o r m s an i n t e r f a c e b e t w e e n t h e s h e l f and t h e a b y s s a l d e p t h s , t h e maximum d e p t h i s s p e c i f i e d as 1000 m e t e r s . 2.1.5 I n s t a l l a t i o n T i m e R e q u i r e m e n t s The i m m e r s i o n t i m e n e c e s s a r y f o r A r c t i c r e g i o n s i s one y e a r b e c a u s e r e c o v e r y i s i m p o s s i b l e d u r i n g t h e w i n t e r . R e c o v e r y o f b o t t o m m o u n t e d i n s t r u m e n t a t i o n i n v o l v e s a c o n s i d e r a b l e e f f o r t i n t h e u s e o f s h i p s and p e r s o n n e l so t h e r e i s a minimum p r a c t i c a l i n s t a l l a t i o n t i m e . A c o n v e n i e n t r e c o r d l e n g t h f o r p u r p o s e s o f t i d a l a n a l y s i s i s one month and t h i s p e r i o d i s c h o s e n as a minimum i m m e r s i o n t i m e . 2.2 S p e c i f i c a t i o n s From an I m p l e m e n t a t i o n P o i n t o f V i e w 2.2.1 R e q u i r e d R e s o l u t i o n o f P r e s s u r e M e a s u r e m e n t The p h y s i c a l p a r a m e t e r m e a s u r e d by t h e t i d e g a uge i s p r e s s u r e w h i c h c a n be r e l a t e d t o d e p t h as -P ( Z , t ) = P Q ( t ) +. g< p(t)> Z ( t ) 2.1 where P o ^ t ^ = a t m o s p h e r i c p r e s s u r e <^p(t)/ >= d e p t h a v e r a g e d d e n s i t y o f s e a w a t e r A f i r s t o r d e r v a r i a t i o n i n d e p t h r e s u l t s i n AP(Z) = <P>gAZ 2:2 Given a s p e c i f i e d r e s o l u t i o n in terms of depth , equat ion 2.2 def ines the requ i red r e s o l u t i o n in the cor responding pressure measurement. One cent imeter has been chosen as a re ference accuracy and i t i s standard p r a c t i c e to inc rease the p r e c i s i o n of the measurement to an order of magnitude beyond the r e f e r e n c e . A r e s o l u t i o n of one m i l l i m e t e r , which represents a s t a b i l i t y of one par t in 10 at 100 meters depth , i s near the l i m i t i n g s e l f - n o i s e of the t ransducer used (Snodgrass 1968). t a k i n g AZ = 10" 3 m 2 g = 9 .8 m/sec < p > = 1 . 0 3 x l 0 3 k g / m 3 The requ i red pressure r e s o l u t i o n i s ^ AP(Z) = 10 Pa 2.3 2 . 2 . 2 Corresponding Reso lu t ions Necessary fo r C o r r e c t i o n s to Data Since bottom pressure i s a f u n c t i o n of P Q as we l l as depth , c o r r e c t i o n s f o r barometr ic pressure f l u c t u a t i o n s may be necessary . The r e s o l u t i o n of barometr ic pressure requ i red to c o r r e c t the water pressure data to an e q u i v a l e n t of one m i l l i m e t e r of depth i s AP = 10 Pa 2.4 o 1 9 ? 10 Pasca ls (Pa)4 10 Newton meter" = 0.0015 pounds inch =• 0.10 m i l l i b a r s 9 In p r a c t i c e , barometr ic pressure i s not known to such a high p r e c i s i o n f o r the f o l l o w i n g reasons : f i r s t , the weather s t a t i o n i s u s u a l l y some d i s tance from the t i d e gauge l o c a t i o n r e s u l t i n g i n phase d i f f e r e n c e s between the two i n s t a l l a t i o n s . Second, the gauge i s i n v a r i a b l y l o c a t e d in a remote area where weather s t a t i o n s record pressure at s i x hour i n t e r v a l s which i s not adequate f o r i n t e r p o l a t i o n to the des i red r e s o l u t i o n . One can only hope that the var iance in t roduced by making c o r r e c t i o n s to t i d a l data i n t h i s manner i s smal l enough so that the data i s not a p p r e c i a b l y b i a s e d . r e l e v a n t parameter a f f e c t i n g marine t r a f f i c , which i s c a l c u l a t e d from measured pressure accord ing to equat ion 2.1 (with removal of barometr ic e f f e c t s ) . Accuracy of the convers ion i s dependent on knowledge of v a r i a t i o n s in depth averaged water At a depth of 100 meters and 10 Pasca ls pressure r e s o l u t i o n , The Hydrographer i s concerned with water h e i g h t , the dens i t y which are r e l a t e d to the d e s i r e d pressure r e s o l u t i o n by A < p ( t ) ) = 0.01 kg In terms of the oceanographic s p e c i f i c g r a v i t y parameter , at, t h i s becomes A ( o ^ ) = 0.01 10 Not only must (<* )^ data be known to t h i s extreme p r e c i s i o n , i t must be sampled as of ten as t i d a l d a t a . In a d d i t i o n , must be known over the complete water column in order to a r r i v e at the depth averaged v a l u e , <(a^) • D e t a i l e d knowledge of dens i t y v a r i a t i o n s i s u s u a l l y not a v a i l a b l e f o r c o r r e c t i o n s to ampl i tude data and, f o r t h i s reason , c o r r e c t i o n s are not normal ly a p p l i e d . In h i g h l y s t r a t i f i e d water near the c o a s t , p ressure - conver ted ampli tudes are s i g n i f i c a n t l y l i m i t e d in accuracy at t i d a l f r e q u e n c i e s . The Oceanographer, however, may be concerned wi th the "raw" pressure record s ince "the t i d a l pressure f l u c t u a t i o n s on the sea f l o o r r e f l e c t we l l the mass v a r i a t i o n s of the water column, and t h e i r measurement i s more fundamental than that of sur face e l e v a t i o n s " ( F i l l o u x 1971) . Since the fundamental q u a l i t y being measured i s p r e s s u r e , re fe rences to t i d a l he ights in t h i s paper are convers ions from pressure as def ined by equat ion 2 . 1 . 2 . 2 . 3 Transducer Requirements , A t i d e gauge mounted on the f l o o r of the c o n t i n e n t a l s h e l f which i s s e n s i t i v e to pressure i s r e s t r i c t e d to measurement of abso lute p r e s s u r e . Absolute pressure can be detected d i r e c t l y w i th an abso lute pressure t ransducer or an e q u i v a l e n t measurement can be made with a d i f f e r e n t i a l t r a n s -ducer arranged to have one port open to a re ference p r e s s u r e . The r e s u l t s from both techniques are comparable but the 11 absolute t ransducer i s much s imp le r to implement. At the time t h i s work was s t a r t e d (1971) only two abso lu te pressure t ransducers were cons idered addquate f o r use as the sensor . The f i r s t , a Hewle t t -Packard quartz c r y s t a l t ransducer was r e l a t i v e l y u n t r i e d at that time and was a l s o f a i r l y expens ive . This t ransducer has s ince proved to have e x c e l l e n t c h a r a c t e r i s t i c s f o r use as an abyssal t i d e gauge ( I r i s h and Snodgrass 1972). The second, a V ib ro t ron t r a n s d u c e r , was 2 chosen because i t s c h a r a c t e r i s t i c s are wel l known , i t i s r e l a t i v e l y i n e x p e n s i v e , and, of equal importance , the s t a f f of the I n s t i t u t e of Oceanography have had exper ience with the t r a n s d u c e r . The V i b r o t r o n conta ins a tungsten wire about one c e n t i -meter in length s t r e t c h e d i n a magnetic f i e l d and enclosed in a dry atmosphere at low p ressure . One end of the wi re i s at tached to a r i g i d frame with the other end connected to a diaphragm. Under p r e s s u r e , the diaphragm i n f l e c t s caus ing tens ion of the wire and i t s na tu ra l f requency of v i b r a t i o n to decrease . With the wi re connected i n the feedback loop of an a m p l i f i e r , a v a r i a b l e frequency o s c i l l a t o r r e s u l t s whose frequency i s a f u n c t i o n of p r e s s u r e . The reader i s r e f e r r e d to the f o l l o w i n g p u b l i c a t i o n s : L e f c o r t 1968, Ro l fe 1968, Snodgrass 1968, N. 0 . I. C. 1968, C a l d w e l l , Snodgrass , and Winbush 1969. 12 2 . 2 . 4 Time Base S t a b i l i t y The e f f e c t of an e r r o r in the time base of a t i d e gauge mani fes ts i t s e l f in two ways: f o r a l i n e a r d r i f t i n t i m e , t i d a l s p e c t r a l components are s h i f t e d i n the amount of the d r i f t ra te and f o r a random e r r o r in time the spec t ra are b l u r r e d (Godin 1973). These e f f e c t s are important when a mechanical c lock i s used but are i n s i g n i f i c a n t when time i s der i ved from a quartz c r y s t a l o s c i l l a t o r . A c r y s t a l time re fe rence i s necessary to measure the output of the V i b r o t r o n t ransducer which r e l a t e s frequency to pressure so that the quartz c r y s t a l serves a dual purpose- that of a master c lock and that of a pressure r e f e r e n c e . I f the t ransducer has a s e n s i t i v i t y of f i v e Hertz per meter and the d e s i r e d depth r e s o l u t i o n i s one m i l l i m e t e r then the t ransducer output must be measured to a p r e c i s i o n of 0.005 H e r t z . With a t ransducer center frequency of 10 k i l o H e r t z , the c r y s t a l re fe rence must be s t a b l e to w i t h i n 0 .5 par ts per m i l l i o n (ppM). Bulova prov ided CMOS c r y s t a l o s c i l l a t o r s wi th the f o l l o w i n g s p e c i f i c a t i o n s Frequency: 447392.427 Hz ( = 2 " / 1 0 minute) Age ing : 0.5 ppM/year Temperature: 0 .5 ppM/°c t u r n - o v e r temperature : - l ° c Power: 3 ma @ 12 v ± 5% 13 2 . 2 . 5 Recording System The recorder chosen f o r the t i d e gauge was a Kennedy DSP 340 which i s an incremental d i g i t a l recorder with seven t racks at 200 charac te rs per i n c h , fea tu res IBM c o m p a t i b i l i t y , and requ i res four ampere-hours per 300 f e e t of tape at 12 v o l t s . The data format on tape c o n s i s t e d of two numbers f o r each sample r e a d i n g - t h e f i r s t being pressure and the second being a time so that each .pressure measurement was a s s o c i a t e d wi th a unique t i m e . To f u r t h e r inc rease s e c u r i t y of the data one channel was reserved f o r a word address in order to d i s t i n g u i s h pressure from t ime. Refer to f i g u r e 2.1 f o r an o u t l i n e of the format . Although t h i s format i s CHANNEL PRESSURE TIME SI S2 S3 S4 S5 DATA DATA DATA DATA DATA WORD ADDRESS PARITY MUX STATE Figure 2.1 Format of Data Wr i t ten on Tape not e f f i c i e n t in terms of data s t o r a g e , the technique does e x h i b i t the f o l l o w i n g f e a t u r e s : a) The combination of the time tag word and the word address b i t ensures immediate r e s y n c h r o n i z a t i o n of the 14 data with rea l time i f charac te rs are missed dur ing the read o p e r a t i on. b) The time tag word acts as a c o n t r o l v a r i a b l e s ince i t s value i s p r e d i c t a b l e . An occas iona l p e r s i s t a n t data b i t e r r o r in the i n s t r u m e n t , r e c o r d e r , or tape reader can be uniquely i d e n t i f i e d and a l lows fo r e a r l y r e p a i r of a f a u l t y component. S t a t i s t i c a l e r r o r i n f o r m a t i o n i s a lso prov ided by the c o n t r o l word which r e f l e c t s the p r o b a b i l i t y of e r r o r s in pressure d a t a . c) In s i t u c a l i b r a t i o n of the c r y s t a l o s c i l l a t o r i s achieved using the time tag word. The procedure c o n s i s t s of s t a r t i n g the instrument c lock us ing WWV rad io as a time r e f e r e n c e , not ing the p r e c i s e time ( v i a WWV) of the l a s t reading p r i o r to shut down, and reading the f i n a l time word. With t h i s technique the c a l i b r a t i o n can be accurate to w i t h i n 0 .5 ppM using a time base of only one month. The method, of c o u r s e , prov ides only an average frequency e r r o r over the time base used. The features ( a ) , (b) above i n d i c a t e an a n t i c i p a t e d problem in reading the data and, as the s e c t i o n on data recovery w i l l show, t h i s was the case . 15 Chapter I I I SAMPLING CONSIDERATIONS 3.1 T radeof fs to Consider in Sampling Techniques The V i b r o t r o n t ransducer has a t r a n s f e r f u n c t i o n r e l a t i n g pressure- to frequency so that the problem of measuring pressure i s t r a n s f e r r e d to one of measuring f requency . In p r a c t i c e , e i t h e r frequency or per iod can be sampled and there are t r a d e o f f s to cons ider wi th regard to the two c h o i c e s . Consider the f o l l o w i n g : i f a s i g n a l of frequency F i s gated i n t o a counter f o r a time T the t o t a l count i s The f i r s t order s e n s i t i v i t y of count (n) wi th respect to any v a r i a b l e (Z) i s Only one of F,T can be al lowed to v a r y - r e s u l t i n g in two possi b i 1 i t i es n = FT 3.1 dn _ - F 3 l dZ -3'Z + T I E 8Z 3.2 = F dT dZ 3 .3 dn = T ^ 1 dZ dZ 3.4 Equation 3 .3 represents a per iod measurement whi le equat ion 3.4 represents a frequency measurement, as i m p l i e d by the 16 s u b s c r i p t on (n ) . 3 . 1 . 1 The Sampling C i r c u i t Before pursuing t h i s matter i t i s necessary to in t roduce the bas ic measurement c i r c u i t used i n the t i d e gauge as dep ic ted in f i g u r e 3 . 1 . In the ensuing d i s c u s s i o n , p o s i t i v e l o g i c i s assumed, components are CMOS, and counters are b inary r i p p l e . Operat ion of the sampling c i r c u i t n I I I I I I S GZ)— 0 R Cl i • < — ° * \ «i— D Q —< > G3>1 m i 1 Figure 3.1 Bas ic Sampling C i r c u i t i n f i g u r e 3.1 i s q u i t e s i m p l e ; i f c o n t r o l l i n e S i s in the high s t a t e , counters C l , C 2 are held in the r e s e t mode, and the f l i p - f l o p output i s low thus d i s a b l i n g gates G2,G3. Counter C2, in the reset mode, has i t s output stage (m) in the low s t a t e . When S goes low, the counter rese ts are removed and gate GI i s enab led . The next r i s i n g edge of s i g n a l F 9 w i l l set the f l i p - f l o p thus enab l ing gates G2,G3 and 17 a l l o w i n g counters Cl ,C2 to accumulate pulses on f a l l i n g edges of s i g n a l F - . , F 2 < F i n a l l y , counter C2 accumulates m l 2 " p u l s e s , stage (m) goes high and gate GI i s d i s a b l e d . The next r i s i n g edge of F2 w i l l reset the f l i p - f l o p which in turn d i s a b l e s gates G2,G3 and stops the count . The time taken f o r counter C2 to accumulate 2m~^ c y c l e s i s „m- l T9 = 4 3 .5 c r 2 whi le the t o t a l count in Cl i s n = F 1 T 2 3 .6 Compare equat ion 3.6 to equat ion 3 . 1 . The sampler desc r ibed e x h i b i t s two unique f e a t u r e s : a) the c o n t r o l S and the s i g n a l need not be synchronized s ince the sampler does t h i s a u t o m a t i c a l l y . b) the aperture time T2 requ i red to take the sample (n) i s a p r e c i s e m u l t i p l e of the per iod of F2. S u b s t i t u t i o n of equat ion 3.5 in to 3.6 y i e l d s F 2 m - l n = p-! 3.7 I f the s i g n a l F2 i s a constant c lock frequency (F c ) and F. i s the V i b r o t r o n s i g n a l (F ) a frequency measurement r e s u l t s 18 I f the r o l e s of F| and are r e v e r s e d , a per iod measurement r e s u l t s : F 2 " - i n T = -f 3 .9 v where (k) has rep laced (m) 3 . 1 . 2 Reso lv ing the Tradeof f Question Returning to the quest ion of t r a d e o f f s between frequency and pe r iod measurement, f i r s t order s e n s i t i v i t i e s of equat ions 3.8 and 3.9 are i i i i f . - ! _ ! ! . 3.10 dZ F dZ c d " T _ F c 2 k " ] dA dZ F V 2 dZ The corresponding aperture times are 3.11 T 2 m _ 1 F = -j 3.12 c 19 I t i s i n s t r u c t i v e to compare aperture time f o r the two techniques at a common s e n s i t i v i t y : l e t dnp dn j dZ dZ 3.14 then ,m-k 3.15 Taking the r a t i o of aperture times and us ing equat ion 3.15 y i e l d s 3.16 A s u i t a b l e value f o r the V i b r o t r o n frequency (F ) i s 10 kHz and the c r y s t a l frequency (F c ) i s near 500 kHz. Equation 3.16 shows that T F = 5 0 Ty 3.17 Therefore the t r a d e o f f to cons ider between frequency and per iod measurement i s that of d i f f e r e n c e s i n aper ture time and consequent e f f e c t s on the d a t a . For a t ransducer s e n s i t i v i t y of f i v e Hertz per meter and one mil 1imeter 1 east s i g n i f i c a n t b i t r e s o l u t i o n , an aperture time of f i v e minutes i s requ i red f o r frequency measurement. The corresponding value f o r per iod measurement at a t ransducer frequency of 10 k i l o K e r t z i s approx imate ly s i x seconds. E i t h e r technique e f f e c t i v e l y c a l c u l a t e s the mean t ransducer frequency dur ing the aperture time thereby p r o v i d i n g some f i l t e r i n g a c t i o n on hiigh frequency components conta ined i n the pressure s i g n a l . Frequency sampling i s c o n s i d e r a b l e more e f f e c t i v e as a f i l t e r . Converse ly , a longer aperture time reduces the maximum p o s s i b l e sample rate thereby l i m i t i n g Nyquist frequency of the d a t a . I t was cons idered advantageous to achieve a high frequency response with the t i d e gauge ra ther than f i l t e r the low-energy h igh - f requency p o r t i o n of the spectrum. Both per iod and frequency measurement could have been i n c o r p o r a t e d wi th the sampling c i r c u i t used, but t h i s would compl icate opera t ion of the instrument which deters from an aim of s i m p l i c i t y . For these reasons the per iod measurement technique was chosen. The sampling c i r c u i t of f i g u r e 3.1 e x h i b i t s a unique e r r o r d e t e c t i o n c a p a b i l i t y when used in a per iod measurement mode: A noise pulse coupled to the low l e v e l V i b r o t r o n s i g n a l can cause an increment to occur in counter C2, r e s u l t i n g in a modi f ied aperture time of 21 Equation 3.9 prov ides the modi f ied sample n'y , F C ( 2 k " 1 - D " T — T ~ The r e s u l t i n g e r r o r in the sample i s A n T = n-j- - n'y F _ _c F v An^ = 50 c yc le s J u d i c i o u s choice of l e a s t count s e n s i t i v i t y fo r the sampling c i r c u i t ensures that the change in sample n^ from one reading to the next i s s i g n i f i c a n t l y l e ss than 50 c y c l e s , r e s u l t i n g i n d e t e c t i o n of e r r o r s of t h i s type . 22 Chapter IV INVESTIGATION OF INSTRUMENTAL AND NATURAL DATA FILTERING The t o t a l wave spectrum of the ocean e f f e c t i v e l y covers ten decades of f requency , from the very long per iod t r a n s t i d a l waves to the very shor t per iod c a p i l l a r y waves. The t i d e gauge descr ibed in t h i s paper measures the lower p o r t i o n of the t o t a l spectrum. Some knowledge of the upper p o r t i o n of the spectrum and i t s e f f e c t on measured data i s c r i t i c a l f o r proper i n t e r p r e t a t i o n of the measured spectrum. Some high frequency wave energy i s a l i a s e d to the measured band and the amount of a l i a s e d energy present in that band i s determined in part by the "net" low-pass f i l t e r f u n c t i o n a p p l i e d to the d a t a . Both ins t rumenta l and natura l f i l t e r i n g occur and together form a composite f i l t e r . 4.1 F i l t e r i n g E f f e c t of S igna l Averaging Whether per iod or frequency measurement techniques are used f o r sampling the t i d a l s i g n a l , the aper ture time remains f i n i t e . S ince the input s igna l i s e f f e c t i v e l y averaged f o r the dura t ion of the aperture "window", a p o r t i o n of the wave spectrum i s removed. The form of t h i s averaging f i l t e r w i l l now be examined. 23 l e t f ( t ) = pressure input s i g n a l f ( t ) averaged fo r T seconds at T second i n t e r v a l s and sampled every T seconds. f T ( t ) note that then and f(nT) f ( t ) < T nT + f f ( t ) dt nT E s ( t - nT) f (nT) n = -oo T Consider a s i n g l e F o u r i e r component of f ( t ) fk ( t ) = fk exp(j\ t ) The i n t e g r a l y i e l d s 4.1 4.2 where f k (nT) = S a ( ^ ) fk (nT) Sa(x) s i n (x) 4.3 and O). T f k ( t ) = S a ( - | - ) E fk (nT) 6( t - nT) U l . T = S a ( - | - ) f k ( t ) 6 T ( t ) 4.4 where « T ( t ) = E 6 ( t - nT) n = -oo The F o u r i e r t ransform of equat ion 4.4 i s F T k ( . ) - - f s a ( ^ ) [ F k ( . k ) * 6u U ) ] 4.5 where and * £ convo lu t ion opera t ion 2TT 24 Summing over a l l F o u r i e r components of f ( t ) y i e l d s F («o) = | s a ( ^ ) [F(co) * « (oo)] 4 .6 o The spectrum of the sampled but non-averaged input s i g n a l has the form (Lath i 1968 page 90) F. (to) = \ [F(to) * 6 U ) ] 4.7 5 I OJ 0 Comparison of equat ions 4 .6 and 4.7 show that the spectrum of the input s i g n a l has been modi f ied by the sampling f u n c t i o n Sa( -^ ) which e f f e c t i v e l y acts as a low-pass f i l t e r with the f o l l o w i n g c h a r a c t e r i s t i c s : a) The envelope of Sa( -^ ) r o l l s o f f wi th a f i r s t order s lope fo r | OJ | > ^ b) Sa(*y) goes to zero at u> = n = ±1, ± 2 , . . . c) Isaty 1)! has a l o c a l maximum at u = ( 2 n ^ ) T r n = ±1 ,±2 , . . . The sampling f u n c t i o n i s s l i g h t l y more e f f e c t i v e than a f i r s t 2 order low-pass f i l t e r wi th a breakpoint at u = — . The high frequency p o r t i o n of the wave spectrum i s dominated by w i n d - d r i v e n swel l wi th t y p i c a l ampl i tudes in the order of one meter . This data i s a l i a s e d to lower f requenc ies unless i t i s removed by f i l t e r i n g . With the swel l occuping a frequency band of about 200 to 700 c y c l e s per hour , and one m i l l i m e t e r r e s o l u t i o n in the pressure measurement, the averaging f i l t e r prov ides f o r three to ten d e c i b e l s a t t e n u a t i o n of swel l f o r per iod measurement and 35 to 45 d e c i b e l s fo r frequency measurement. 25 4 . 2 N a t u r a l F i l t e r i n g i n the Ocean 4 . 2 . 1 F i l t e r i n g A c t i o n o f Deep Water The ocean wate r column behaves as a low pass f i l t e r to passage o f w i n d - g e n e r a t e d waves . A t t e n u a t i o n o f s u r f a c e wave p r e s s u r e f l u c t u a t i o n s i n c r e a s e s w i t h i n s t r u m e n t depth and wave f r e q u e n c y . The v a r i a b l e measured by the t i d e gauge i s p r e s s u r e so t h a t a c o n v e n i e n t t r a n s f e r f u n c t i o n to d e s c r i b e the f i l t e r f u n c t i o n i s one t h a t r e l a t e s wave p r e s s u r e on the sea f l o o r to ( u n a t t e n u a t e d ) p r e s s u r e j u s t below the s u r f a c e o f the o c e a n . Development o f the t r a n s f e r f u n c t i o n f rom the Navi e r - S t o k e s e q u a t i o n v i a B e r n o u l l i ' s i s c l a s s i c a l and i s not r e p e a t e d here (see Kinsman 1965 page 1 4 1 ) . U s i n g the s m a l l a m p l i t u d e a p p r o x i m a t i o n ^ , the t r a n s f e r f u n c t i o n r e l a t i n g g a i n to depth (h) and f r e q u e n c y (w) i s e x p r e s s e d i n p a r a m e t r i c form as H(u>,k) = [ c o s h ( k h ) ] - 1 4 . 8 2 = gk [ t a n h ( k h ) ] 4 . 9 where k 2jT x = r a d i a n wave number and X = w a v e l e n g t h For s m a l l a m p l i t u d e s , wave h e i g h t i s much l e s s than wave l e n g t h . For most g r a v i t y waves t h i s i s a good a p p r o x i m a t i o n . 26 The ocean i s a remarkable f i l t e r as can be seen from f i g u r e 4 . 1 , having a s lope of about 300 d e c i b e l s per decade at 60 d e c i b e l s a t t e n u a t i o n . For i n s t a l l a t i o n s near the maximum 4 0 1 1 — WIND-GENERATED V SWELL 1 \ - \o \ ° r V \ o \-o \ -A \ l \ o \3 i 1 -10' I0 2 FREQUENCY cy/hr lO 3 10 Figure 4.1 A t t e n u a t i o n of the Pressure E f f e c t of Surface Waves as Measured on the Sea F loor as a f u n c t i o n of Frequency and Depth depth of 1000 meters most of the energy from wind-generated swel l i s removed whi le at 10 meters much of the wave energy remains. 4 . 2 . 2 A t t e n u a t i o n of Swel l by Sea Ice The i c e cover of the A r c t i c Ocean forms a boundary l a y e r between a i r and water , r e s u l t i n g in a wave spectrum which i s c o n s i d e r a b l y d i f f e r e n t from that of i c e - f r e e oceans. Short wavelength components of a sea p e n e t r a t i n g i c e are r a p i d l y at tenuated wh i le l o n g - p e r i o d waves are s t i l l d e t e c t a b l e severa l hundred k i l o m e t e r s i n t o the i c e (Wadhams 1973) . 27 In a d d i t i o n to e x t e r n a l l y generated s w e l l , l o c a l barometr ic f l u c t u a t i o n s and winds may cause waves in sea i c e (Hunkins 1962). FREQUENCY cy/hr Figure 4.2 Genera l i zed Amplitude Spectrum of Waves on the A r c t i c Ocean ( a f t e r Hunkins 1962) wi th the E f f e c t of Depth F i l t e r i n g Included The ampli tudes of these waves are qu i te s m a l l , the order of one cent imeter or l e s s , so that contaminat ion of t i d a l data i s b a r e l y s i g n i f i c a n t . F igure 4.2 shows the ampl i tude spectrum of measured waves i n the A r c t i c Ocean (Hunkins 1962) wi th the e f f e c t s of depth f i l t e r i n g i n c l u d e d . With a sample i n t e r v a l of f i v e minutes , o f f s h o r e t i d e gauge r e s u l t s w i l l over lap the spectrum of f i g u r e 4.2 by one decade which may prov ide f o r an extens ion of the g e n e r a l i z e d spectrum down to t i d a l f r e q u e n c i e s . 28 Chapter V ELECTRONIC AND MECHNICAL DESIGN 5.1 E l e c t r o n i c Design Compl ementary -meta l -ox ide - semi conductor (CMOS) l o g i c was chosen f o r the t i d e gauge f o r i t s very low power requi rements . Quiescent power d i s s i p a t i o n i s t y p i c a l l y three orders of magnitude below that of comparable b i p o l a r c i r c u i t s , wh i le dynamic power consumption i s a f u n c t i o n of frequency and load c a p a c i t a n c e . Other features of CMOS l i e in areas of n o n - c r i t i c a l supply v o l t a g e s , high noise immunity, medium speed c a p a b i l i t i e s , and high f a n - o u t . Complete c i r c u i t diagrams are provided in Appendix 1 and some design fea tu res of the c i r c u i t s are presented below. CONTROL and SAMPLING CIRCUITS: Timing opt ions such as sample r a t e , w r i t e f requency , record gap s e l e c t , and s e n s i t i v i t y s e l e c t are on the c i r c u i t boards in the form of wire jumpers s i n c e these s e t t i n g s are fundamental to opera t ion of the instrument and are not normal ly changed once connected. A l l tape recorder c o n t r o l s are superv ised by the master t im ing l i n e in an asynchronous manner to ensure recovery from a l o g i c e r r o r w i t h i n o n e - h a l f of a sampl ing i n t e r v a l . 29 MANUAL CONTROLS: The master c o n t r o l panel was designed wi th an aim f o r s i m p l i c i t y . Instrument opera t ion i s i n i t i a t e d with a s i n g l e l o c k i n g s w i t c h , the reset/run c o n t r o l fo r c l o c k count-down c i r c u i t s . While in the rese t mode, the reset/run c o n t r o l a u t o m a t i c a l l y i n i t i a l i z e s the tape recorder c i r c u i t s . Other manual c o n t r o l s inc lude push buttons f o r : generat ion of EOF gaps, s lewing the tape (and EOR gap) , and an enable c o n t r o l f o r the sample i n d i c a t o r . A l l c o n t r o l s are mounted on a small panel l o c a t e d near the tape recorder i n t e r l o c k l e v e r which f i x e s the tape c a r t r i d g e in p l a c e . A l l swi tches are connected to ground in t h e i r normal opera t ing s t a t e s and are shunted wi th a r e s i s t o r to ensure a ground connect ion in case of minor swi tch contact c o r r o s i o n . SIGNAL CONDITIONING: The V i b r o t r o n s i g n a l i s c o n d i t i o n e d by an o p e r a t i o n a l t ransconductance a m p l i f i e r (OTA) o p e r a t i n g in an open loop mode as a comparator. The output of the V i b r o t r o n i s passed through one s ide of the OTA. The re ference input of the a m p l i f i e r i s a lso used to clamp the a -c coupled V i b r o t r o n output . In t h i s way the a -c component of the V i b r o t r o n s i g n a l can be ex t rac ted in the presence of c o n s i d e r a b l e d r i f t in the re ference l e v e l . This ensures a symmetric output from the d i f f e r e n t i a l a m p l i f i e r . H y s t e r e s i s i s provided by a low-pass f i l t e r a t t e n u a t i n g the input s i g n a l , phase s h i f t i n g i t 90 degrees, and adding i t to the d -c re ference 1 evel . 30 POWER SUPPLY and REGULATION: Power i s provided by three hard- topped lead a c i d b a t t e r i e s (wi th low s p e c i f i c - g r a v i t y a c i d ) in an o i l bath which i s open to ambient pressure v ia a neoprene diaphragm. One bat te ry i s d i v i d e d in to two sets of three c e l l s , thus p r o v i d i n g two independent vo l tage s u p p l i e s at 12 and 18 v o l t s each which are diode i s o l a t e d i n case of f a i l u r e of one supp ly . The 12 v o l t supply prov ides power f o r the l o g i c and tape recorder wh i le the 18 v o l t l e v e l s u p p l i e s the vo l tage r e g u l a t o r s . Current d r a i n on the 18 v o l t supply was e igh t mi 11iamperes and on the 12 v o l t s u p p l y , l e s s than one m i l l i a m p e r e . Approx imately 70 ampere-hours i s requ i red fo r one y e a r ' s o p e r a t i o n . The vo l tage r e g u l a t o r s share a temperature-compensated zener re ference diode such that the net e f f e c t of vo l tage changes on the c r y s t a l o s c i l l a t o r i s n e g l i g i b l e r e l a t i v e to i t s s t a b i l i t y s p e c i f i c a t i o n . The t o t a l e f f e c t on the V i b r o t r o n due to wors t - case input vo l tage changes i s an order of magnitude below the l e a s t count l i m i t of one m i l l i m e t e r and the r e g u l a t o r ' s i n d i r e c t temperature e f f e c t on the V i b r o t r o n i s n e g l i g i b l e i n comparison to the d i r e c t e f f e c t of ambient temperature. 5.2 Mechanical Design The mechanical layout of the t i d e gauge i s best seen by r e f e r r i n g to f i g u r e 5 . 1 . The pressure housing dimensions were 107 cent imeters long by 28 cent imeters in diameter and c o n s i s t e d of two compartments. The s m a l l e r pr imary chamber 31 conta ined the V ib ro t ron wi th a m p l i f i e r , s i g n a l c o n d i t i o n e r , and diode i s o l a t o r s fo r the power supp ly . The secondary chamber conta ined the e l e c t r o n i c s wi th tape recorder and was i s o l a t e d from the primary by a bulkhead in order to p r o t e c t the system from e f f e c t s of a t ransducer or b a t t e r y cable penet rator l e a k . A f i b e r g l a s s box of dimensions 57 cent imeters long by 31 cent imeters wide by 30 cent imeters high conta ined the o i l immersed b a t t e r i e s . The l i d df the ba t te ry case c o n s i s t e d of a neoprene diaphragm under a p o l y v i n y l c h l o r i d e p l a t e c o n t a i n i n g v e n t i l a t i o n holes to a l low t r a n s m i s s i o n of ambient pressure to the o i l b a t h . The support frame was cons t ruc ted of welded angle i r o n and was 122 cent imeters by 152 c e n t i m e t e r s . L i f t i n g lugs were prov ided in each corner fo r attachment of a s t e e l cable s l i n g . The complete u n i t had a weight e q u i v a l e n t to 300 k i lograms in a i r and 150 ki lograms in water . Components of the frame and housing in contact were made from m a t e r i a l s of s i m i l a r l e v e l in the e l e c t r o c h e m i c a l a c t i v i t y s e r i e s to minimize e f f e c t s of Ga lvan ic c o r r o s i o n . In a d d i t i o n , the s t e e l pressure housing was coated with epoxy to l i m i t chemical c o r r o s i o n . However, the epoxy coat had a thermal expansion c o e f f i c i e n t d i f f e r e n t from that of s t e e l -r e s u l t i n g in f l a k i n g of the p r o t e c t i v e c o a t . Figure 5.1 Exploded View of the Cont inenta l She l f Tide Gauge 33 Chapter VI CALIBRATION PROCEDURES AND RESULTS 6.1 C a l i b r a t i o n Procedure The pressure sensing element of the t i d e gauge c o n s i s t s of a V i b r o t r o n t ransducer and i t s a s s o c i a t e d a m p l i f i e r which together have a t r a n s f e r f u n c t i o n r e l a t i n g frequency to a p p l i e d p r e s s u r e . The t r a n s d u c e r , however, i s a l so s e n s i t i v e to ambient temperature wh i le the a m p l i f i e r e x h i b i t s some vo l tage s e n s i t i v i t y . When making high r e s o l u t i o n pressure measurements the secondary s e n s i t i v i t i e s become s i g n i f i c a n t and some knowledge of them i s r e q u i r e d . The pressure c a l i b r a t i o n was e f f e c t e d by m a i n t a i n i n g constant vo l tage with a monitored re ference source and approx imate ly constant temperature with a la rge water ba th . The pressure source was a dead-weight t e s t e r wi th a copper tube to t r a n s m i t pressure to the t ransducer which was conta ined in a small w a t e r - t i g h t housing immersed i n the water bath . The bath was cooled with i ce and repeated pressure c a l i b r a t i o n s were c a r r i e d out as the water warmed. The thermal time constant of the water bath was about 10 hours so that the temperature changed by l e s s than 0.5 degrees C e l s i u s dur ing a c a l i b r a t i o n . Using a c a l i b r a t e d frequency counte r , readings were taken f o r both i n c r e a s i n g and decreas ing pressure at equal time i n t e r v a l s . E f f e c t s of a l i n e a r temperature d r i f t in 34 the c a l i b r a t i o n curve were minimized by averaging the r i s i n g and f a l l i n g curves . The time requ i red f o r a s i n g l e c a l i b r a t i o n was v a r i e d and t h i s al1 owed removal of temperature dependence in the h y s t e r e s i s curve fry- assumi ng : a l i n e a r d r i f t in temperature dur ing the c a l i b r a t i o n . A d e t a i l e d vo l tage c a l i b r a t i o n was performed at atmospheric pressure and gross c a l i b r a t i o n s were inc luded with the pressure c a l i b r a t i o n s . An independent temperature c a l i b r a t i o n was done at atmospheric pressure by c o o l i n g an i n s u l a t e d t ransducer and c a l i b r a t e d t h e r m i s t o r i n a f r e e z e r . Barometr ic pressure was monitored dur ing a l l c a l i b r a t i o n s in order to provide an abso lute re fe rence f o r the d a t a . 6.2 A n a l y s i s of C a l i b r a t i o n Data C a l i b r a t i o n s were performed on three V ib ro t ron t ransducers of which one had a maximum pressure of 70x10 Pasca ls (10^ pounds per square inch) and the others had a maximum of 3.5x10 Pasca ls (500 pounds per square i n c h ) . The t ransducers are r e f e r r e d to in what f o l l o w s by a combination of the manufacturer ' s i n i t i a l s and the device s e r i a l number so that the high pressure V ib ro t ron was designed UC173 with the others ass igned BJ5811 and UC92, where UC r e f e r s to United Contro l Corporat ion and BJ r e f e r s to B . J . E l e c t r o n i c s . Most pressures are expressed in terms of e q u i v a l e n t water depth to provide a bas is f o r compar ison. 35 6 . 2 . 1 Voltage and Temperature C a l i b r a t i o n s 51 The vo l tage s e n s i t i v i t i e s were p r i m a r i l y dependent on the a m p l i f i e r s manufactured by Sundstrand Data C o n t r o l . The values f o r the two a m p l i f i e r s were near - 1 . 0 cent imeter per v o l t at 12 v o l t s and adequate operat ion was achieved over a supply range of 10 to 20 v o l t s . Only a s l i g h t dependence on opera t ing pressure was n o t i c e d . The net e f f e c t of b a t t e r y vo l tage supply v a r i a t i o n s a f t e r r e g u l a t i o n to w i t h i n a few m i l l i v o l t s was n e g l i g i b l e . C r o s s - p l o t t i n g temperature and pressure data prov ided temperature s e n s i t i v i t y as a f u n c t i o n of opera t ing p ressure . I t was f e l t , however, that t h i s technique d id not prov ide r e l i a b l e data s ince repeated a p p l i c a t i o n of maximum pressure cyc les r e s u l t e d in very small o f f s e t s i n the c a l i b r a t i o n curve which requ i red a number of hours to d i s s a p p e a r 1 , These o f f s e t s tended to d i s t o r t the pressure dependency of temperature s e n s i t i v i t y . Work by others has i n d i c a t e d that changes in temperature s e n s i t i v i t y are g e n e r a l l y l e s s than 10 percent over 2 the f u l l s c a l e pressure range . Temperature s e n s i t i v i t y v a r i e d with the p a r t i c u l a r t ransducer but was c o n s i s t a n t f o r an i n d i v i d u a l d e v i c e . The measured s e n s i t i v i t i e s at atmospheric p r e s s u r e , v i r t u a l l y independent of the a m p l i f i e r used, were as fo l1ows: H y s t e r e s i s was t y p i c a l 1 y 0.02 per cent . Snodgrass (personal communicat ion) . 36 337.0 cm °C (UC173) 23.1 cm (UC92) + 19.4 cm (BJ5811) The t i d e gauge i s normal ly used in con junc t ion with a cu r ren t meter which a lso measures temperature to w i t h i n 0.03 degrees c o r r e c t i o n of t i d a l data to approx imately 0 .5 cent imeter f o r UC92 and BJ5811. The accuracy of UC173 a f t e r temperature c o r r e c t i o n i s only 10 cent imeters and f o r t h i s reason UC173 was not used in a permanent i n s t a l l a t i o n . 6 . 2 . 2 A n a l y s i s of Pressure C a l i b r a t i o n Data S t r u c t u r a l a n a l y s i s of the V i b r o t r o n t ransducer i n d i c a t e s the form of the t r a n s f e r f u n c t i o n r e l a t i n g pressure (P) to frequency ( F v ) should be a polynomial of the form ( L e f c o r t 1968) where a ,c are constants f i t t e d to the c a l i b r a t i o n d a t a . I t was decided to t e s t t h i s theory by f i t t i n g f i v e d i f f e r e n t po lynomials to the d a t a . A measure of accuracy of the f i t was provided by standard d e v i a t i o n of d i f f e r e n c e s between C e l s i u s . Using the S* values and temperature data a l lows P = 37 exper imental pressure readings and c a l c u l a t e d v a l u e s . A 3 r e l a t i v e f i g u r e of mer i t r e p r e s e n t i n g complex i ty of the polynomial was provided by the product of number of constants in an equat ion with order of the p o l y n o m i a l . The t e s t polynomials and a s s o c i a t e d f i g u r e s of mer i t (FoM) were as f o l l o w s : FoM Test Equation 2 P = a + b F v 6.1 4 P = a+ c F v 2 6.2 6 P = a + b F y + c F v 2 6 .3 12 P = a + b F v + c F y 2 + d F y 3 6 .4 20 P = a + b F y + c F y 2 + d F y 3 + e F v 4 6 .5 F igure 6.1 i l l u s t r a t e s the r e s u l t s wi th standard d e v i a t i o n (normal ized with respect to maximum pressure to which the c a l i b r a t i o n s were c a r r i e d ) p l o t t e d aga ins t r e l a t i v e f i g u r e of meri t . A s t a t i s t i c a l accuracy 1 i m i t f o r the c a l i b r a t i o n data i s represented by the l e v e l of the p lateau achieved f o r each of the curves in f i g u r e 6 . 1 . The accuracy l i m i t represents r e s t r i c t e d p r e c i s i o n of frequency measurements r a t h e r than "F igure of mer i t " i n t h i s context i s used p r i m a r i l y to i d e n t i f y the p a r t i c u l a r p o l y n o m i a l . 38 absolute accuracy of the t ransducer or dead-weight t e s t e r . The "best " c a l i b r a t i o n curve has a low standard d e v i a t i o n and, in a d d i t i o n , i s not too complex. The f i g u r e 10 O Q I- LU < N > LU < ^ rc 11 CO ^ I L BJ58II 10 ' h 10 0 •20 UC92 UCI73 0 20 FIGURE OF MERIT Figure 6.1 Standard Dev ia t ion of C a l i b r a t i o n Data Versus C a l i b r a t i o n Curve Complexity of mer i t f o r the opitimum equation appears at the elbow of the curves of f i g u r e 6.1 and the corresponding optimum equat ions f o r each of the transducers a r e : equat ion 6.3 fo r BJ5811, UC92 4 and equat ion 6.2 f o r UC173 . The maximum c a l i b r a t i o n pressure f o r UC173 was only 20 per cent of rated p ressure . For BJ5811 and UC92 the cor responding values were 110 per cent and 100 per cent r e s p e c t i v e l y . 39 A summary of constants fo r the c a l i b r a t i o n equat ions i s provided in tab l e I. Table I C a l i b r a t i o n Constants f o r V ib ro t ron Transducers Transducer Equation 6.2 Equation 6 .3 a c a b c kPa kPa kPa kPa kPa ( k H z ) 2 kHz ( k H z ) 2 UC92 15083.0 -118 .815 13869.9 232.238 -129 .875 BJ5811 15251.3 - 8 7 4 . 4 8 3 14676.9 298.197 - 9 1 2 . 9 6 3 UC1 73 84965.5 -268 .445 Accuracy of c a l c u l a t e d t i d a l he ights from the c a l i b r a t i o n equat ion i s s i g n i f i c a n t l y dependent on the choice of c a l i b r a t i o n p o l y n o m i a l . Represent ing a change in t i d a l amplitude as a measured frequency excurs ion ( A F v ) from a qu iescent opera t ing po int (F ) , . t h e d i f f e r e n c e (e) in excurs ion pressures as c a l c u l a t e d from equat ions 6.2 and 6 .3 i s e = A P 6 . 3 - A P 6 . 2 E ^ b 6 f 3 + 2 ( c 6 i 3 - c 6 - 2 ) F V ] A F V For a t i d a l ampl i tude of three meters , the d i f f e r e n c e (e) can be as la rge as two cent imeters depending on i n s t a l l a t i o n depth. 40 Chapter VII IN SITU TESTS AND DATA RECOVERY 7.1 P r a c t i c a l Aspects of F i e l d Tests Instrument prototypes must o i l t i m a t e l y be removed from the secure env i rons of the l a b o r a t o r y and placed in the sometimes hazardous rea l w o r l d . In s i t u t e s t s of a t i d e gauge such as the one descr ibed here r e q u i r e s a c o n s i d e r a b l e e f f o r t in the form of l o g i s t i c s , p e r s o n n e l , and t ime . A t e s t per iod of one month was cons idered adequate f o r an e s t i m a t i o n of instrument performance s ince t i d a l harmonic a n a l y s i s r e q u i r e s a record length of one lunar month fo r proper separa t ion of dominant t i d a l components. 7 . 1 . 1 Choosing a Test Region The f o l l o w i n g f a c t o r s were cons idered i n the choice of l o c a t i o n f o r f i e l d t r i a l s : a) A tempera tu re - reco rd ing cur rent meter was not a v a i l a b l e , thus the prime q u a l i f i c a t i o n fo r the t e s t l o c a t i o n was that of r e l a t i v e l y constant temperature. b) Reasonably accurate barometr ic data f o r the reg ion had to be a v a i l a b l e . c) Some knowledge of expected mean water d e n s i t y v a r i a t i o n s was requ i red f o r proper i n t e r p r e t a t i o n of r e s u l t s . 41 d) The l o c a t i o n had to be near enough to the l a b o r a t o r y to permit overn ight r e p a i r s , i f r e q u i r e d , and to a l low f o r f requent readings of the water height s t a f f . Upper Howe Sound and Saanich i n l e t were cons idered as p o s s i b l e l o c a t i o n s s ince both are f i o r d - t y p e e s t u a r i e s having deep water and are p ro tec ted from ex te rna l temperature i n f l u e n c e s by a s i l l . Saanich i n l e t had fewer d e n s i t y v a r i a t i o n s and more a c c u r a t e 1 barometr ic records than upper Howe Sound but Saanich I n l e t , l o c a t e d i n south Vancouver I s l a n d , was d i f f i c u l t to access from the l a b o r a t o r y which was l o c a t e d on the mainland at the U n i v e r s i t y . Upper Howe Sound was chosen as the main t e s t s i t e . 7 . 1 . 2 I n s t a l l a t i o n and Recovery Techniques The two instrument housings were designed to wi thstand a maximum pressure of IO'7 P a s c a l s , e q u i v a l e n t to a depth of 1000 meters . P r i o r to complete instrument t e s t s , the housings were pressure tes ted to a depth of 550 meters fo r a per iod of two hours. The procedure fo l lowed f o r l a y i n g and r e t r i e v i n g the t i d e gauge was s i m i l a r to a standard technique adopted by the Hydrographic Se rv i ce f o r i n s t a l l a t i o n of cu r rent meters . F igure 7.1 d e p i c t s the p h y s i c a l arrangement on the sea f l o o r fo r the t e s t s e r i e s in Howe Sound. The t i d e gauge was lowered "More accura te" because Saanich I n l e t i s c o n s i d e r a b l y c l o s e r to a permanent weather s t a t i o n than i s upper Howe Sound. 42 to the sea f l o o r f i r s t , fo l lowed by the anchor , then the buoy. For c o n t i n e n t a l s h e l f or A r c t i c i n s t a l l a t i o n s a subsurface cu r ren t meter was suspended above the t i d e gauge, the buoy was absent , and an a c o u s t i c r e l e a s e device was placed between the ground l i n e and the anchor . I f the buoy i s l o s t or the a c o u s t i c re lease f a i l s to o p e r a t e , the ground l i n e serves as a secondary recovery system. F igure 7.1 Typ ica l Tide Gauge I n s t a l l a t i o n f o r Howe Sound Test S e r i e s No problems were encountered wi th the i n s t a l l a t i o n method used. However, the l a r g e mass of, the pressure housing (150 k i lograms) proved somewhat d i f f i c u l t to handle dur ing s e r v i c e p e r i o d s . The s i z e and mass of the complete instrument requ i red that a l l shipboard d isassembly and assembly had to be done outdoors . 7.2 Other F i e l d Tests Related to the Tide Gauge P r i o r to f i n a l c o n s t r u c t i o n of the c o n t i n e n t a l s h e l f t i d e gauge, the b a s i c concepts of the inst rument were t e s t e d by breadboarding a sha l low -water ve rs ion of the o f f s h o r e gauge. The temporary model c o n s i s t e d of a low pressure (2x10^ Pasca ls ) V i b r o t r o n t ransducer and a m p l i f i e r mounted i n a small pressure housing and connected to the e l e c t r o n i c s wi th a c a b l e . The output frequency of the V i b r o t r o n was sampled, converted to an analogue vo l tage and recorded on char t paper. An e igh t day s e r i e s of data was c o l l e c t e d in August 1972 at the permanent t i d e gauge i n s t a l l a t i o n i n Tsawwassen, B r i t i s h Columbia. Comparisons between the permanent f l o a t gauge and s h a l l o w - w a t e r gauge prov ided an e r r o r d e v i a t i o n l e s s than one c e n t i m e t e r . Subsequent to c o n s t r u c t i o n and t e s t i n g the o f f s h o r e t i d e gauge a second v e r s i o n of the sha l low -wate r gauge us ing the same t ransducer was breadboarded f o r the purpose of measuring se iches in San Juan harbour at Port Renfrew, B r i t i s h 2 Columbia . Two sampling c i r c u i t s were incorpora ted in the wave gauge, both of which operated in a cont inuous mode. One sampler measured the V ib ro t ron frequency at a low r e p e t i t i o n rate of 0.05 Hertz wh i le the other measured per iod at a high rate of one H e r t z . The output of each sampler was s p l i t i n t o two o v e r l a p p i n g e igh t b i t numbers thus p r o v i d i n g 2 Instrument d e t a i l and data w i l l be presented in D. Lemon's MSc t h e s i s ( to be completed) 44 both high and low r e s o l u t i o n wave d a t a , the r a p i d sampler y i e l d i n g the t o t a l wave spectrum and the slow sampler p r o v i d i n g a low passed vers ion of the spectrum. The four samples were placed in ho ld ing r e g i s t e r s , converted to analogue v o l t a g e s , and s tored by a f requency-modulated tape r e c o r d e r . The tapes were then demodulated i n the l a b o r a t o r y wi th e x i s t i n g equipment, d i g i t i z e d , and s to red on n i n e - t r a c k tape . The record ing scheme was somewhat i n d i r e c t but r e s u l t e d in c o m p a t i b i l i t y wi th e x i s t i n g d a t a - p r o c e s s i n g f a c i l i t e s at the I n s t i t u t e of Oceanography. Two s e r i e s of data have been c o l l e c t e d to d a t e , in August 1973 a n d ' i n Februrary 1974. I n i t i a l r e s u l t s were encourag ing , with wave he ights of l e s s than one m i l l i m e t e r detected as we l l as t i d a l waves of four meters h e i g h t , r e p r e s e n t i n g an e f f e c t i v e dynamic measurement range in excess of four decades cover ing n e a r l y f i v e decades of f requency . 7.3 Recovery of Of fshore T i d a l Data The sampling t e c h n i q u e , data format on t a p e , n o n l i n e a r t ransducer response, and necessary data c o r r e c t i o n s combined to y i e l d a fo rmidable problem of data reduct ion in order to a r r i v e at a time s e r i e s of t i d a l h e i g h t s . A number of programs were w r i t t e n to process the data in l o g i c a l s t e p s . The f u n c t i o n a l contents of the programs are descr ibed below f o r r e f e r e n c e . 45 7TC0N: Read the seven^track i instrument tape , - checked f o r missed tape c h a r a c t e r s , reformated the data to IBM INTE6ER*2, and wrote on a n i n e - t r a c k output tape. This program a l s o provided output of any des i red record i n decimal on a l i n e p r i n t e r . Wr i t ten in assembly language f o r the PDP-12 at the 3 I n s t i t u t e of Oceanography . TRANS: Prov ided d i a g n o s t i c in fo rmat ion on recorded time d a t a . WRPRND: Removed f u l l - s c a l e wraparounds i n sampled data and res to red most s i g n i f i c a n t po r t ion of samples, which was not recorded . DEGLCH: Prov ided e r r o r d i a g n o s t i c s on sampled d a t a . E r r o r d e t e c t i o n was e f f e c t e d by known bounds on data from one sample to the next . Attempts at c o r r e c t i o n were made, based on known c h a r a c t e r i s t i c s of the sampling c i r c u i t . F a i l u r e to recover r e s u l t e d in present reading being set equal to previous sample. CONVRT: Converted sampled data to V ib ro t ron frequency v i a sampler t r a n s f e r f u n c t i o n . Corrected frequency values fo r time s e r i e s temperature s e n s i t i v i t y . Converted frequency values to pressure us ing the t ransducer c a l i b r a t i o n e q u a t i o n . BAROPR: Corrected pressure record f o r barometr ic pressure time s e r i e s . L i n e a r i n t e r p o l a t i o n s were c a l c u l a t e d on a i r o 7TC0N was w r i t t e n by M. M i l l a r , then s t a f f programmer at the I n s t i t u e of Oceanography. 46 p r e s s u r e r e c o r d . C o n v e r t e d p r e s s u r e r e c o r d t o t i d a l h e i g h t t i m e s e r i e s . GENREC: P r o d u c e d a t i d a l r e c o r d a t a n y d e s i r e d s t a r t t i m e , o u t p u t s a m p l e r a t e , and number o f o u t p u t s a m p l e s . P e r f o r m e d l i n e a r i n t e r p o l a t i o n s on i n p u t r e c o r d . T h i s p r o g r a m was a l s o i n c o r p o r a t e d i n t o many o f t h e d a t a a n a l y s i s r o u t i n e s . I n c l u s i o n o f a s e p a r a t e c h a n n e l t o r e c o r d a t i m e - t a g w o r d f o r e a c h p r e s s u r e m e a s u r e m e n t p r o v e d t o be a v e r y u s e f u l t e c h n i q u e f o r o p t i m i z i n g i n s t r u m e n t p e r f o r m a n c e . The p r o g r a m TRANS p r o v i d e d d i a g n o s t i c i n f o r m a t i o n t h a t l e d t o d e t e c t i o n o f a f a u l t y m u l t i p l e x e r c o m p o n e n t t h a t had an e r r o r r a t e o f l e s s t h a n 0 .1 p e r c e n t . The p r o g r a m DEGLCH and a n a l o g u e p l o t s o f t h e s a m p l e d d a t a l e d t o r e l o c a t i o n o f t h e V i b r o t r o n s i g n a l - c o n d i t i o n i n g c i r c u i t t h u s r e m o v i n g a s o u r c e o f n o i s e w h i c h had been c o u p l e d f r o m t h e d i g i t a l c i r c u i t s t o t h e V i b r o t r o n s i g n a l , r e s u l t i n g i n d a t a e r r o r r a t e o f 1 . 5 p e r c e n t . The number o f t a p e c h a r a c t e r s m i s s e d d u r i n g a r e a d o p e r a t i o n as d e t e c t e d by 7TC0N and TRANS o c c u r r e d a t a r a t e o f 0 . 3 p e r c e n t . T h i s e r r o r r a t e was a l s o r e f l e c t e d i n t h e p r e s s u r e d a t a as d e t e c t e d by DEGLCH b u t t h e p r e c i s e c a u s e was n o t d e t e r m i n e d . 47 Chapter VIII ANALYSIS OF TEST RESULTS The c o n t i n e n t a l s h e l f t i d e gauge prototypes underwent f i e l d t r i a l s from June 26, 1973 to September 18, 1973. Data s e l e c t e d f o r d e t a i l e d a n a l y s i s c o n s i s t e d of two f i n a l i n s t a l l a t i o n s of the gauge c o n t a i n i n g V ib ro t ron t ransducer UC92. Both i n s t a l l a t i o n s occurred near B r i t a n n i a Beach, B r i t i s h Columbia, l o c a t e d on upper Howe Sound. The f i r s t s e r i e s , designated HOI, s t a r t e d at 12 :26 :15 PST J u l y 3 0 , stopped at 1 0 : 2 1 : 5 0 PST August 7, and the t e s t p o s i t i o n was 49° 37' 38" north by 123° 12' 50" west. Mean inst rument depth was 146.95 meters . The second s e r i e s , H02, was at the same p o s i t i o n in a depth of 173.19 meters , s t a r t e d at 1 2 : 4 8 : 4 5 PST August 7, and stopped at 23 :28 :35 PST September 13. F igure 8.1 prov ides a map of the t e s t region whi le f i g u r e 8.2 i s an amplitude p l o t of the two s e r i e s . The sample i n t e r v a l f o r both s e r i e s was 0.625 minutes . Barometr ic c o r r e c t i o n s to the data were der i ved from weather records at Vancouver I n t e r n a t i o n a l A i r p o r t , a d i s tance of 45 k i lomete rs from the t e s t s i t e . A i r pressure samples were at s i x hour i n t e r v a l s and l i n e a r i n t e r p o l a t i o n s were a p p l i e d f o r in te rmed ia te v a l u e s . Gross temperature c o r r e c t i o n s were der ived from oceanographic s t a t i o n Howe 4.5 monthly data r e c o r d s . A p a r a b o l i c f i t was a p p l i e d to the J u l y , August , Figure 8.1 Upper Howe Sound Showing L o c a t i o n of Test S i t e Figure 8.2 T i d a l Time Ser ies Used fo r Data A n a l y s i s 50 and September temperature readings fo r in te rmed ia te v a l u e s . Maximum temperature v a r i a t i o n f o r the three monthly readings was 0.1 degrees C e l s u i s . Time dependent d e n s i t y c o r r e c t i o n s , usefu l fo r shore based water height compar isons , were not a p p l i e d because of i n s u f f i c i e n t d a t a . Densi ty values a v a i l a b l e from the three monthly samples at S t a t i o n Howe 4 .5 i n d i c a t e d the p o s s i b i l i t y of pressure to depth convers ion d i s c r e p e n c i e s as la rge as f i v e c e n t i meters . 8.1 Resu l ts of Harmonic A n a l y s i s A subset of the s e r i e s H02 was generated at hour ly i n t e r v a l s and c o n s i s t e d of 793 data po in ts centered at zero hours PST August 26, 1973. This data was subjected to a harmonic a n a l y s i s program provided by the Marine Sciences D i r e c t o r a t e , P a c i f i c Region. The r e s u l t s are summarized i n Appendix 2 along with t i d a l components at Squamish, nine k i l o m e t e r s north of the t e s t s i t e , and components at Po in t A t k i n s o n , 35 k i lomete rs south of the t e s t s i t e . The analyses performed on re ference s t a t i o n s were based on a record length of one year . Most harmonic components agreed wel l in ampl i tude and phase except f o r d i u r n a l component KI which was about 16 cent imeters low, and semidui rna l component S2 which was about f i v e cent imeters h i g h . The mean d i f f e r e n c e of components between Squamish and the t e s t s i t e , e x c l u d i n g KI and S2 , was - 0 . 0 5 6 cent imeters wi th a 95 per cent conf idence i n t e r v a l of ± 0.296 c e n t i m e t e r s . F o u r i e r t ransform r e s u l t s agreed wel l 51 wi th the harmonic a n a l y s i s ( w i t h i n three cent imeters f o r KI and two cent imeters fo r S 2 ) . The reason f o r d i s c r e p a n c i e s at KI and S2 has not been determined. 8.2 Low Frequency P o r t i o n of the Power Spectrum The record length f o r s p e c t r a l c a l c u l a t i o n s was chosen to represent the fundamental data per iod and to ensure a cont inuous f u n c t i o n at the record end p o i n t s . Record length was 27.969 days and c o n s i s t e d of 65,536 samples. The low frequency por t ion of the power spectrum i s presented as a non-averaged l i n e spectrum in f i g u r e 8 . 3 . Var ious t i d a l spec ies dominated the spectrum at f requenc ies near 0 . 0 4 , 0 . 0 8 , 0 . 1 2 , 0 . 1 6 , 0 . 2 0 , and 0.24 c y c l e s per hour. The continuum of background energy was a l so apparent between t i d a l s p e c i e s , f a l l i n g r e l a t i v e l y smoothly wi th i n c r e a s i n g f requency . Low l e v e l background energy was not a f f e c t e d by the q u a n t i z a t i o n no ise l i m i t which c o i n c i d e d with the h o r i z o n t a l a x i s . The background energy near 0.06 cyc les per hour was somewhat higher than expected. This region of the spectrum, between d i u r n a l and semid iurna l f r e q u e n c i e s , was l i k e l y i n f l u e n c e d by b a r o t r o p i c d i s t u r b a n c e s . The weather was g e n e r a l l y calm dur ing the t e s t per iod except f o r a moderate south wind which o f ten appeared at midday and u s u a l l y p e r s i s t e d u n t i l e a r l y evening . 52 10 8 n 10 cm2- I0~4 cy/hr 0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 IO 4 i 10 .-4 0.14 0.16 0.18 0.20 0.22 F cy/hr 0.24 0.26 0.28 Figure 8 .3 Non-Averaged L ine Power Spectrum of S e r i e s H02 53 8 . 3 High Frequency P o r t i o n of the Power Spectrum The complete power spectrum i s prov ided in f i g u r e 8 . 4 . This spectrum was p l o t t e d using l o g a r i t h m i c averaging in order to improve conf idence l i m i t s at high f r e q u e n c i e s . The most s imple form of log -band averaging i s to average groups in powers of two ( 1 , 1 , 2 , 4 , 8 , 16, . . . ) The scheme can be extended to i n c l u d e subgroups that c o n s i s t s of powers of two as i n ( 1 , 1 , 1 , 1 ) , ( 1 , 1 , 1 , 1 ) , (2 , 2 , 2 , 2 ) , (4 , 4 , 4 , 4 ) , . . . With t h i s method, the t o t a l number of po in ts averaged i s a convenient power of two. In g e n e r a l , i f the o r i g i n a l number of po in ts i s N = 2 n and the s i z e of each subgroup i s M = 2 m then the number of po in ts a r r i v e d at a f t e r t a k i n g means i s p = 2 m (n-m+1) The spectrum of f i g u r e 8.4 was c a l c u l a t e d wi th a subgroup s i z e of 2 3 . The complete power spectrum was dominated by d i u r n a l and semid iu rna l t i d a l components wi th h igher spec ies extending to near l y one c y c l e per -hour. I d e n t i f i c a t i o n of the two or three peaks appearing immediately below one c y c l e per hour as t i d a l harmonics was not c e r t a i n . Above one c y c l e per hour the 54 s p e c t r a l peaks were l i k e l y s e i c h e s . The h ighest frequency resonance peak had a per iod of approx imate ly 8.1 minutes . The fundamental per iod of o s c i l l a t i o n f o r a r e c t a n g u l a r bas in of length (Lv); and depth (h) i s (Defant 1 958 page 61) Taking f o r a length the d i s tance between the s i l l and Woodfibre where the channel t u r n s , (L) and (h) are L = 12 km h = 250 m f o r which T = 8.1 minutes The second h ighest frequency peak, with a per iod of 10.8 minutes , was t e n t a t i v e l y i d e n t i f i e d in a s i m i l a r way as the fundamental component between the s i l l and Squamish, l o c a t e d at the head of Howe Sound. D e t a i l e d examination of a few maximums and minimums in the t i d a l data revealed the occas iona l presence of a t r a n s i e n t o s c i l l a t i o n with a per iod near 10 minutes , s t a r t i n g at s l a c k water and l a s t i n g only a few c y c l e s wi th an ampli tude of approx imately one c e n t i m e t e r . The increase in energy with frequency above 10 c y c les per hour was caused in part by the q u a n t i z a t i o n no ise l i m i t imposed by l i m i t e d measurement r e s o l u t i o n . 55 I 0 " 4 I 0 ' 3 10 2 10 1 I 10 I 0 2 F _ cy/hr Figure 8.4 F u l l Power Spectrum of S e r i e s H02 Featur ing Log-Band Averaging 56 8.4 Comparison of S t a f f Readings and Pressure Gauge Readings Absolute water height re ference data was provided by a s t a f f mounted on a p i e r l o c a t e d one k i l o m e t e r southeast of the t e s t s i t e . Amplitude readings were taken over a 20 hour per iod on August 6 , 7, 1973 and over a short i n t e r v a l on Table II D i f f e r e n c e between Water Surface Leve ls and Pressure Gauge Readings Date Sampling Per iod S t a f f Hei ght Tide State Mean Di f fe rence 95%Confi dence l i m i t s 1973 hours meters c e n t i meters cent imeters Aug 6 2.0 2.519 high - 2 . 5 8 + 0 . 3 1 Aug 6 1 .0 2.296 1 ow 2.84 + 0.33 Aug 6 1 .2 2.976 hi gh 1 . 3 . + 0.14 Aug 7 2.1 0.329 1 ow . - 1 . 5 7 + 0.26 Aug 14 1 .5 0.195 1 ow 1 .51 + 0.64 Sept 8 1.9 0.411 1 ow 0.16 + 0.61 Sept 9 1 .8 0.318 1 ow - 1 .67 + 0.94 August 14, September 8 , and September 9 , 1973. A summary of the comparisons i s provided in t a b l e I I . The mean d i f f e r e n c e s were w i t h i n expected d i s c r e p a n c i e s r e s u l t i n g from depth averaged d e n s i t y v a r i a t i o n s ' and d id not app.ear c o r r e l a t e d with t i d a l h e i g h t . A p r e c i s e s p e c i f i c a t i o n of absolute accuracy was indeterminate from the comparisons due to d e n s i t y e f f e c t s but has an upper bound of three c e n t i m e t e r s . Long term d r i f t of t i d a l data measured was l e s s than four c e n t i -meters per month, based on August 14 and September 8 , 9 comparisons. Time s e r i e s p l o t s f o r the l a s t three comparisons i s presented in f i g u r e 8 . 5 . The s i n u s o i d a l form of September d i f f e r e n c e s was p r i m a r i l y due to sur face waves s ince the pressure gauge response was r e l a t i v e l y smooth over the i n t e r v a l s . A review of the August 6 , 7 comparisons a l so i n d i c a t e d a s i n u s o i d a l tendency in the data but d i s p e r s i o n of data po in ts made t h i s c o n c l u s i o n u n c e r t a i n . The per iod of o s c i l l a t i o n s i n f i g u r e 8 .5 appeared to be i n a range of 50 to 100 minutes , which was a l s o revealed in the power spectrum of f i g u r e 8 .4 with a resonant peak of 71.9 minutes . A numerical i n t e g r a t i o n of the 71.9 minute resonant peak (above background l e v e l s ) y i e l d e d a root -mean-square s i g n a l l e v e l of 0.28 c e n t i m e t e r . The sur face waves of f i g u r e 8 .5 were observed ye t were bare l y detected by the bottom-mounted pressure gauge. This may have been due to s p a t i a l d i f f e r e n c e s in amplitude and pressure measurements or to dynamic d e n s i t y changes i n the water column. 58 € = S T A F F - G A U G E + D A T U M C O R R E C T I O N H O R I Z O N T A L S C A L E S : T I M E IN M I N U T E S Figure 8 .5 Time S e r i e s of D i f f e r e n c e s Between Water Surface Leve ls and Pressure Gauge Readings f o r S e r i e s H02 59 Chapter IX SUMMARY AND RECOMMENDATIONS Knowledge of t i d e s on the c o n t i n e n t a l s h e l f i s usefu l to both Oceanographer and Hydrographer. The Oceanographer requ i res boundary c o n d i t i o n s fo r h is l a r g e - s c a l e t i d a l models and est imates of the continuum of energy, d i f f i c u l t to measure i n noisy c o a s t a l r e g i o n s , c o n t r i b u t e towards c a l c u l a t i o n s of oceanic energy d i s s i p a t i o n . The Hydrographer uses o f f s h o r e . data to p r e d i c t t i d a l he ights at c o a s t a l ports both d i r e c t l y and i n d i r e c t l y , where t i d a l i n f o r m a t i o n from the c o n t i n e n t a l s h e l f serves as input to mathematical models of c o a s t a l r e g i o n s . In the A r c t i c Ocean, ex tens i ve i ce cover o f ten prec ludes the , use of shore -based t i d a l i n s t r u m e n t a t i o n . The bottom-mounted t i d e gauge prototype d e s c r i b e d i n t h i s t h e s i s has a r e s o l u t i o n c a p a b i l i t y of one m i l l i m e t e r , which corresponds to a dynamic measurement range of one part per . m i l l i o n at 1000 meters depth. A s i n g l e unattended i n s t a l l a t i o n y i e l d s f i v e frequency decades of wave i n f o r m a t i o n wi th an abso lute accuracy of amplitude measurement dependent on secondary parameters such as sea f l o o r temperature and depth averaged d e n s i t y . S i g n a l - t o - n o i s e r a t i o fo r the gauge can approach 60 d e c i b e l s at t i d a l f r e q u e n c i e s . Spect ra of waves measured with the c o n t i n e n t a l s h e l f t i d e gauge are 60 sub jec t to low pass f i l t e r i n g from natura l causes such as depth a t t e n u a t i o n and from sampling techn iques . The V ib ro t ron t ransducer provides a frequency output that i s modulated by the pressure s i g n a l . E i t h e r frequency or per iod can be sampled, depending on the t r a d e o f f between d e s i r a b l e low pass f i l t e r i n g of wind waves or a requirement f o r a high Nyquist f requency . The l a t e r fea tu re was chosen f o r the t i d e gauge. Carefu l a t t e n t i o n was paid to the choice of c a l i b r a t i o n polynomial with the r e s u l t that a s l i g h t l y more compl icated polynomial improved accuracy of ampl i tude measurements by as much as two c e n t i m e t e r s . Design of the s i g n a l p rocess ing elements were guided by an aim fo r s i m p l i c i t y and r e l i a b i l i t y , w i th redundancy i n both c o n t r o l and data s t o r a g e . Recording a ; t i m e - t a g word with each pressure measurement prov ides fo r immediate recovery from l o s t data and, in a d d i t i o n , y i e l d s s t a t i s t i c a l i n f o r m a t i o n on instrument o p e r a t i o n . The mechanical aspect of the instrument package, though i n e l e g a n t , was f u n c t i o n a l . F i e l d t e s t r e s u l t s i n d i c a t e d adequate performance but were somewhat l i m i t e d with regard to s p e c i f i c a t i o n v e r i f i c a t i o n on a f i n e s c a l e due to s i g n i f i c a n t water d e n s i t y v a r i a t i o n , making p r e s s u r e - t o - d e p t h convers ions of r e s t r i c t e d v a l i d i t y . I n e q u a l i t i e s between sur face wave measurementssand corresponding bottom pressure data i n d i c a t e s the p o s s i b l e presence of unusual time dependence in water column d e n s i t y 61 s t r u c t u r e of the t e s t r e g i o n . Oceans cover ing the c o n t i n e n t a l s h e l f do not e x h i b i t the r e l a t i v e l y extreme d e n s i t y v a r i a t i o n s at t i d a l f requenc ies observed in the t e s t r e g i o n . As est imate of l i m i t i n g s e l f noise of the t ransducers would have been usefu l f o r e v a l u a t i o n of abso lute inst rument performance. One procedure to obta in the l i m i t i s to p lace two or more t ransducers in a the rmal l y q u i e t envi ronment , c o r r e c t the r e s u l t i n g records fo r temperature e f f e c t s to an extreme p r e c i s i o n , remove coherent energy between t ransducers with s p e c t r a l methods, and examine the remaining noncoherent energy which represents s e l f - l i m i t i n g noise of the t ransducers ( I r i s h and Snodgrass 1972). The two prototypes cons t ruc ted f o r t h i s p r o j e c t were permanently i n s t a l l e d i n the Beaufor t Sea of the A r c t i c Ocean in October , 1973. Recovery of the f i r s t data s e r i e s i s a n t i c i p a t e d in August , 1974. 62 BIBLIOGRAPHY B a t c h e l o r , G.K. F l u i d Dynamics. Cambridge: Cambridge U n i v e r s i t y P r e s s , 1970 Bendat, J u l i u s S . , and A l l a n G. P i e r s o l . Random Data: A n a l y s i s and Measurement  Procedures . New York: W i 1 e y - i n t e r s c i e n c e , 1971 C a l d w e l l , Douglas R., Frank E. Snodgrass, and Mark W. Wimbush. "Sensors i n the Deep S e a , " Phys ics Today, Vol 22 , No 7 J u l y 1969 C h a p p e l l , R.W. " V i b r o t r o n Absolute Pressure T ransducer , " Borg-Warner C o n t r o l s . B u l l e t i n VF-8150-562 C0S/M0S In tegrated C i r c u i t s Manual , RCA Technica l S e r i e s CMS-270, 1971 Defant , A l b e r t . Ebb and Flow. Ann Arbor : U n i v e r s i t y of Michigan P r e s s , 1958 F i l l o u x , J . H . "Deep Sea Tide Gauge with O p t i c a l Readout of Bourdon Tube R o t a t i o n s , " Nature , Vol 226 , June 6, 1970 F i l l o u x , Jean H. "Deep Sea Tide Observat ions from the Northeastern P a c i f i c , " Deep Sea Research, Vol 18, 275 -284 , 1971 F r a n k i g n o u l , Claude J . and R.F. Henry. S p e c t r a l A n a l y s i s of Short I n e r t i a l - I n t e r n a l Wave Records. Marine Sc iences D i r e c t o r a t e , Manuscr ipt Report S e r i e s #34, 1973 Godin, G a b r i e l . The A n a l y s i s of T i d e s . Toronto: U n i v e r s i t y of Toronto P r e s s , 1972 Godin , G a b r i e l . E ight Years of Observat ions on the Water Level  at Quebec and Grandines 1962-1969 Par t 1 - A n a l y s i s of the  T ida l S i g n a l . Marine Sciences D i r e c t o r a t e , Manuscr ipt Report S e r i e s #31, 1973 Guttman, I rwin and S . S . W i l k s . In t roductory Eng ineer ing  S t a t i s t i e s . New York: W i l e y , 1965 H a l l i w e l l , A. R. and T .G. P e r r y . "E r ro rs i n Tide Gauges," The Dock & Harbour A u t h o r i t y . Vol XLVI11 No 568, Feb 1968 BIBLIOGRAPHY . (cont inued) Hunkins , Kenneth. "Waves on the A r c t i c Ocean," Journa l of  Geophysical Research. Vol 67, No 6, June, 1962 I r i s h , J . D . and F .E . Snodgrass. "Quartz C r y s t a l s as M u l t i -purpose Oceanographic S e n s o r s - I . P r e s s u r e , " Deep Sea  Research. Vol 19 , ( 1 6 5 - 1 6 9 ) , 1972 Operat ion and Maintenance Manual Model DSP 340 Recorder , " Kennedy Co. , 1967 Kinsman, B l a i r . Wind Waves. Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l 1 , 1965 L a t h i , B .P . Communication Systems. New York: W i l e y , 1968 L e f c o r t , M.D. " V i b r a t i n g Wire Pressure Transducer Technology, Journal of Ocean Technology, Vol 2 , No 2, 1968 Lennon, G.W. "The I n t e r p r e t a t i o n of Van de Castee le Diagrams, I n s t i t u t e of Coastal Oceanography and T i d e s . ICOT/IR/8, 1 966 Lennon, G.W. "The Behaviour of a S t i 1 1 i n g - W e l 1 i n the Presence of P e r i o d i c Dens i ty V a r i a t i o n s , " I n s t i t u t e of  Coasta l Oceanography and T i d e s . ICOT/IR/7, 1966 LeSchack, Leonard A. and Richard A. Haubr ick . "Observat ions of Waves on an Ice -Covered Ocean," Journal of  Geophysical Research. Vol 69, No 18, 1964 Munk, W. and D. C a r t w r i g h t . " T i d a l Spectroscopy and P r e d i c t i o n , " P h i l . T rans . Royal S o c i e t y of London," A 259. (533-581) 1966 Munk, Walter H. and Bernard D. Z e t l e r . "Deep-Sea T i d e s : A program," S c i e n c e . Vol 158, Nov 17, 1967 P i c k a r d , George L. D e s c r i p t i v e P h y s i c a l Oceanography. Oxford Pergamon P r e s s , 1963 R o l f e , R.C. " V i b r a t i n g Wire Pressure Transducer E l e c t r o n i c s , " Journal of Ocean Technology. Vol 2 , No 2. 1968 Snodgrass, Frank E. "Deep-Sea Instrument C a p s u l e , " S c i e n c e . Vol 162, Oct , 1968 BIBLIOGRAPHY (cont inued) U.S. Navy Oceanographic Ins t rumentat ion Cente r , Vi brot ron  Pressure Transducer , Instrument Fact Sheet #68011, Mar, 1968 Wadhams, P e t e r . "A t tenuat ion of Swell by Sea I c e , " Journal  of Geophysical Research. Vol 78, No 18, June , 1973 APPENDIX 1 Cont inenta l S h e l f Tide Gauge C i r c u i t Diagrams 66 o O _l o o o _l o Q -z. < _ J o cc o o CD CC UJ h-< X CD O U J U J _l CO WRITE/STEP SLEW EOR EOF MUX CONTROL TIME REFERENCE START END co U J J O C O U J 2 : o cc r -o o U J cc ^ U J U J Q cc £ o o ± ! U J cc O U J < cc CL < h- r -T T cc U J X - J U J <t —I t CL -R Q — I ID T T I I PRESSURE >-o -z. U J Z> o U J cc cc U J < C O < CRYSTAL OSCILLATOR 447392.43 Hzl R AI3 15 18 21 24 25 26 27 28 R Tl T2 T3 T4 T5 T6 T7 R <f> BI2 T8 T9 TIO Til TI2 TI3 TI4 MASTER CONTROL SWITCH SAMPLE INDICATOR CONTROL , 2 2 0 ,5 .6 K PB SLEW PB • SLEW EOF 6.4v >56K n =J=O.I MANUAL SLEW CONTROL C3 <f> Q D Q C3 4> CLK AlON .Rj S8 JAI^> c AIO> « - S 8 „ MASTER RESET GATES E N D - O F - F I L E PULSE GENERATOR MULTIPLEXER AND BUFFER TPI T P 3 D 0 A 6 <f> Q I 1 t 1 t t t — i t t t t t M PI P2 P 3 P 4 P 5 P6 P7 4> A 3 R - C C A 8 P8 P 9 PIO PI I PI2 PI3 PI4 <£ A 2 R A 5 II 12 13 14 T P 2 T P 4 PI5 4> A l R c/> A 4 15 16 17 18 19 2 0 21 SENSITIVITY S E L E C T FREQUENCY S A M P L E R V VIB OUT STATIC GND rfn TRANSDUCER AND AMPLIF IER VOLTAGE r*-VB REGULATOR VIBROTRON LOGIC a 0 RECORDER I2v •GND CO POWER SUPPLY VOLTAGE REGULATOR SIGNAL CONDITIONER CO MPONENT ID PART ENTIFICATION NUMBER DEVICE DESCRIPTION A B C D 7 16,21 CD4001AE Quad two input NOR 1 CD4002AE Dual four input NOR 4 CD4007AE Dual complimentary p a i r p lus i n v e r t e r 8,11 17,19 2 CD4011AE Quad two input NAND 6 14 ,18 ,20 1 ,3 CD4013AE Dual D f l i p f l o p 2 - 9 CD4016AE Quad b i l a t e r a l switch 15 CD4017AE Synchronous decade counter 5 ,12 ,13 CD4020AE Binary r i p p l e counter 14 stage 1 - 4 11 ,12 ,13 CD4024AE Binary r i p p l e counter 7 stage 10 CD4049AE Hex i n v e r t i n g buf fer 10 CD4050AE Hex n o n - i n v e r t i n g bu f fe r 2 CA3080 Micropower programmable OTA 22 CA3082 NPN array 5,6 UA776 Micropower programmable Op Amp --> C APPENDIX 2 dal Components at the B r i t a n n i a Beach Test S i t e and Reference S t a t i o n s as Determined by Harmonic Analys 72 APPENDIX 2 T ida l Components at the B r i t a n n i a Beach Test S i t e and Two Reference S t a t i o n s as Determined by Harmonic A n a l y s i s T i d a l Component Name Squamish B r i tann ia Beach P t . A tk inson * Ampli tude Phase Ampli tude Phase Ampli tude Phase cm + 0.015 deg cm + 0.15 deg cm + 0.015 deg Mm 1.5 50.6 0.9 271 .3 6.4 112.9 MSf 1.0 256.1 1.5 240.8 2.8 79.1 2QT 1.2 132.9 2.7 120.0 1 .3 141 .9 *1 7.4 148.3 6.7 131 .4 7.4 146. 5 °1 49 .3 152.7 49.7 151 .3 47.5 151.0 N 0 ] 2.7 145.0 2.4 224.7 4.0 144.3 K l 87.4 166.5 71 .0 182.1 86.6 164.7 J l 5 .3 191 .1 6.1 173.3 5.1 194.6 oo1 3.0 184.1 4 .9 223.5 3.4 202. 3 e 2 0.3 190.9 2N 2 2.9 111.0 1.8 88. 8 2.6 125.7 N 2 19.4 136.4 18.3 129.5 19.4 134.7 M 2 94.2 159.3 94.5 159.5 92.4 158.3 L 2 2.7 194.7 1 .5 15.1 2.9 204.3 S 2 23.2 180.1 28.0 186.1 23.2 178.9 ? 2 0.2 39.5 0.9 235.6 0.4 11.0 M03 0.2 16.1 0.0 84.3 0.1 301 . 6 M 3 0.2 38.4 0 .3 342.5 0.1 13.1 73 APPENDIX 2 (cont inued) T i d a l Component Name Squamish Bn* tanni a Beach P t . A tk inson * Ampli tude Phase Ampli tude Phase Ampli tude Phase cm + 0.015 deg cm + 0.15 deg cm + 0.015 deg MK3 0.5 165.2 0.6 178.2 0.7 183. 6 SK 3 0.1 286.3 0.6 254.0 0 .3 227.1 MN4 0.4 1 38.9 0 .3 1 33.6 0.4 140.9 M 4 0.9 161 .6 0.9 152.5 0.9 164.3 S N 4 0.2 183.4 0.0 164.0 0.1 147.9 MS4 0.4 1 78.6 0 .3 1 99.8 0.5 169.9 2MNg 0.5 37.7 0.6 44 .3 0.7 93.5 M 6 1 .0 70.2 0.9 72. 7 0.9 66.2 2MSg 0.8 92. 9 0.9 101 .9 0.7 93.5 M 8 0.1 81 .8 0.0 77.9 0.1 82.4 * The e r r o r bound on amplitude r e f e r s only to p r e c i s i o n of o r i g i n a l data which was in u n i t s of f e e t . 

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