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.Sc,  University  A THESIS SUBMITTED  of B r i t i s h C o l u m b i a , 1970  IN PARTIAL FULFILMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  In the Department of Electrical  Engineering  We a c c e p t t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  J u n e , 1974  In p r e s e n t i n g an the  this  thesis  in partial  advanced degree at the U n i v e r s i t y Library  I further for  shall  make i t f r e e l y  agree t h a t p e r m i s s i o n  h i s representatives.  of  this  written  gain  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  shall  that  31  May  1974  copying o f t h i s  that  thesis  copying o r p u b l i c a t i o n  n o t be a l l o w e d w i t h o u t  Engineering  Columbia  I agree  by t h e Head o f my D e p a r t m e n t o r  permission.  Electrical  Columbia,  f o r r e f e r e n c e and s t u d y .  f o r extensive  I t i s understood  thesis f o r financial  Department o f  Date  of B r i t i s h  available  s c h o l a r l y p u r p o s e s may be g r a n t e d  by  f u l f i l m e n t o f the requirements f o r  my  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 r e s e n t e d .  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 p e r i o d of one year w i t h a f i v e minute sample r a t e . is  A Vibrotron  absolute pressure  transducer  the s e n s i n g element with p r e s s u r e measured to an e q u i v a l e n t  water h e i g h t of one m i l l i m e t e r . filtering  Instrumental  of wind waves and t r a d e o f f s  are i n v e s t i g a t e d . to provide  useful  performance.  and o c e a n i c  i n sampling techniques  Storage and r e d u c t i o n of data i s statistical  Transducer  i n f o r m a t i o n on i n s t r u m e n t  c a l i b r a t i o n data a n a l y s i s  that careful  c h o i c e of c a l i b r a t i o n polynomial  significantly  improve accuracy of t i d a l d a t a .  and a n a l y s i s of r e s u l t s  arranged  i n d i c a t e adequate  indicates  can In s i t u  tests  instrument  performance, but high p r e c i s i o n c o m p a r i s i o n s between sea bottom pressure and measured water h e i g h t are of value i n the t e s t r e g i o n due to v a r i a t i o n s density.  Spectra r e s u l t s  reveal  distinctive  to the t e s t r e g i o n .  based s t a f f  readings and o f f s h o r e  limited  i n mean water  the presence of  seiches  Comparisions between  p r e s s u r e data i n d i c a t e  p o s s i b l e presence of unusual dynamic water d e n s i t y at the t e s t  site.  shorethe  structure  i i i TABLE OF CONTENTS  Chapter  Page  I  1  INTRODUCTION PREVIOUS WORK  II  3  SPECIFICATIONS OF THE TIDE GAUGE SPECIFICATIONS FROM A HYDROGRAPHIC  4 POINT  OF VIEW  4  A b s o l u t e Accuracy of L o c a l Height of Tide . .  4  S t a b i l i t y of the Measurement  5  Sample Rate Requirements  6  Operating  7  Depth Requirements.  Installation  Time Requirements  7  SPECIFICATIONS FROM AN IMPLEMENTATION POINT OF VIEW  7  Required R e s o l u t i o n of P r e s s u r e Measurements.  7  Corresponding Corrections Transducer  III  R e s o l u t i o n s Necessary  for  to data  Requirements  8 TO  Time Base S t a b i l i t y  12  Recording System  13  SAMPLING CONSIDERATIONS  15  TRADEOFFS TO CONSIDER IN SAMPLING TECHNIQUES.  15  The sampling C i r c u i t  16  R e s o l v i n g the T r a d e o f f Question  18  iv  CONTENTS  (continued)  Chapter IV  Page  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 A t t e n u a t i o n of Swell by Sea Ice V  VI  VII  25 . . . . . . .  ELECTRONIC AND MECHANICAL DESIGN  26 28  ELECTRONIC DESIGN  28  MECHANICAL DESIGN  30  CALIBRATION PROCEDURES AND RESULTS  33  CALIBRATION PROCEDURE  33  ANALYSIS OF CALIBRATION DATA. . . »  34  V o l t a g e and Temperature C a l i b r a t i o n s  35  A n a l y s i s of P r e s s u r e C a l i b r a t i o n Data  36  IN SITU TESTS AND DATA RECOVERY PRACTICAL ASPECTS OF FIELD TESTS  40 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  (continued)  Chapter  Page  VIII  47  ANALYSIS OF TEST RESULTS 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 IX  SUMMARY AND RECOMMENDATIONS  56 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 i b r o t r o n  Transducers.  II  D i f f e r e n c e Between Water S u r f a c e L e v e l s and P r e s s u r e Gauge Readings  39 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  B a s i c Sampling C i r c u i t  16  4.1  A t t e n u a t i o n of the P r e s s u r e E f f e c t of S u r f a c e Waves as Measured on the Sea F l o o r as a F u n c t i o n of Frequency and Depth  26  G e n e r a l i z e d 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 included  27  Exploded View of the C o n t i n e n t a l Gauge  32  4.2  5.1 6.1 7.1  S h e l f Tide  Standard D e v i a t i o n 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 Typical  Tide Gauge I n s t a l l a t i o n  38  f o r Howe  Sound Test S e r i e s  42  8.1  Upper Howe Sound Showing L o c a t i o n of Test S i t e  8.2  Tidal  8.3  Non-Averaged  8.4  F u l l Power Spectrum of S e r i e s H02 F e a t u r i n g L o g Band A v e r a g i n g Time S e r i e s of D i f f e r e n c e s between Water S u r f a c e L e v e l s and P r e s s u r e Gauge Readings f o r S e r i e s H02  8.5  . .  Time S e r i e s Used f o r Data A n a l y s i s L i n e Power Spectrum of S e r i e s H02 . .  48 49 52 55 58  vi i i  LIST OF VARIABLES  Variable  Definition  a  Constant  in c a l i b r a t i o n  equation  b  Constant i n c a l i b r a t i o n  equation  c  Constant i n c a l i b r a t i o n  equation  d  Constant i n c a l i b r a t i o n  equation  e  Constant i n c a l i b r a t i o n  equation  f(t)  Generalized  signal  F  Value of f r e q u e n c y ,  g  A c c e l e r a t i o n of  h  Depth of ocean  H  Pressure t r a n s f e r  j  Square r o o t of -1  k  Integer v a r i a b l e ,  m  Integer  variable  n  Integer  variable  p  Pressure in  P o S^  Barometric Sensitivity  t  Time  T  Time i n t e r v a l ,  e  w  spectrum  gravity  " meter  N  generalized  t  0  function  r a d i a n wave number  s  (= , P a  or P a s c a l )  Pressure of depth re temperature  variable period  (  =  ^)  ix  LIST OF VARIABLES  Variable  Definition  z  Water h e i g h t  6  Impulse  £  Amplitude d i f f e r e n c e  e  Temperature  X  Wavelength  p  Mass d e n s i t y of water  a  t  function  variable  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>  (continued)  Depth averaged value of x  ACKNOWLEDGEMENT Merci to the P r o f e s s o r s , Graduate S t u d e n t s , and S t a f f  of  IOUBC who taught me the what, where, when, and why of  water.  D. E n g l i s h and H. Heckel of Oceanography mechanical p o r t i o n s of the t i d e Mr. S. Wigen, T i d a l  Superintendent,  constructed  gauges. MSD, p r o v i d e d  a d v i c e on t e s t r e s u l t s as w e l l as s t a f f  thoughtful  readings  w h i l e on h o l i d a y s . Dr. J . MacDonald reviewed the e l e c t r o n i c d e s i g n and suggested the format f o r r e c o r d i n g Special  data.  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 g e n t l e 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  level.  G r a t i t u d e t o , and a f f e c t i o n f o r , my c o - a u t h o r ,  co-reseacher,  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  shelf  r e g i o n s over long p e r i o d s of time has been made f e a s i b l e by r e c e n t advances i n the f i e l d of d i g i t a l  electronics.  The  t r a n s d u c e r s and r e c o r d i n g systems r e q u i r e d by s e l f - c o n t a i n e d i n s t r u m e n t packages have been a v a i l a b l e f o r a number of y e a r s but, u n t i l  the advent of c o m p l e m e n t r y - m e t a l - o x i d e - s e m i c o n d u c t o r  (CMOS) t e c h n o l o g y ,  i n s t a l l a t i o n s of l o n g e r 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 , w i t h  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  characteristic  low power requirements has removed a t e c h n o l o g i c a l from the s c i e n c e o f  local  barrier  oceanography.  Why measure t i d a l at a l l ?  h e i g h t s on the c o n t i n e n t a l  shelf  C o a s t a l i n s t a l l a t i o n s p r o v i d e adequate data to  t i d e s and the i n s t r u m e n t a l problems are f a r l e s s  than those of o f f s h o r e i n s t a l l a t i o n s . installations,  however,  shelf contributes  severe  i s i n f l u e n c e d by l o c a l geographic and  of a t i d a l wave along the c o a s t as w e l l installation.  predict  Data from c o a s t a l  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  offshore  its  Tidal  progression  as data from an  h e i g h t data c o l l e c t e d on the  to development of o c e a n i c t i d a l models and  a l s o d e p i c t s the form of long p e r i o d waves trapped by the continental  s h e l f . Mathematical modeling of c o a s t a l  regions  2  can now p r o v i d e a c c u r a t e p r e d i c t i o n s of l o c a l t i d e s i f models are given s u i t a b l e d r i v i n g  functions derived  offshore data.  it  locations,  In A r c t i c r e g i o n s  the  from  i s d i f f i c u l t a n d , i n some  i m p o s s i b l e to measure t i d a l h e i g h t s from shore  based s t a t i o n s d u r i n g the w i n t e r months because of the accumul a t i o n of l a r g e p i e c e s of i c e along the s h o r e . 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  In some r e s p e c t s  i s i d e a l w i t h regard  the data because i n w i n t e r months the e x t e n s i v e filters  pack i c e  much of the wind generated wave energy so t h a t  a l i a s i n g occurs.  to  In summer months the l o w - l y i n g  little  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  tide  gauge can p r o v i d e 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 s u r g e . 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 p r o t o t y p e  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 w i t h a view towards d e t e r m i n i n g e f f e c t i v e performance of instrument.  the  The d e s i g n 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 a c c u r a c y and s t a b i l i t y requirements of the data f o r hydrography p u r p o s e s .  Although  the i n s t r u m e n t i s designed f o r use on any c o n t i n e n t a l 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  shelf,  prototypes  were a c t u a l l y c o n s t r u c t e d as there i s always a p o s s i b i l i t y  of  l o s s of an i n s t r u m e n t due to f l o o d i n g o f the p r e s s u r e housing or f a i l u r e to r e c o v e r the package.  3  1.1  P r e v i ous Work Much of the work i n the f i e l d of o f f s h o r e  tidal  i n s t r u m e n t a t i o n has been concerned w i t h s h o r t - t e r m applications  (see Snodgrass 1968, F i l l o u x  1970).  deep-sea The  importance  of deep-sea t i d a l measurement has been emphasized by Munk and Zetler  (1967).  shelf"* however,  Long-term i n s t a l l a t i o n s o n . t h e  continental  were not c o n s i d e r e d i m p o r t a n t u n t i l  expansion of s h i p p i n g a c t i v i t y Hudson-James Bay r e g i o n s .  the  in the Canadian A r c t i c  In the p a s t , A r c t i c  and  t i d a l data has  been taken from s h o r e - b a s e d s t a t i o n s p r i m a r i l y d u r i n g  the  summer w i t h 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 round.  recent  year-  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  u s i n g sounding techniques from grounded i c e f l o e s by Hunkins  1962).  (described  4  Chapter  II  SPECIFICATIONS OF THE TIDE GAUGE The design of an i n s t r u m e n t 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 d a t a - i n t h i s case the h y d r o g r a p h e r .  The d e s i g n e r 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 implementation of the r e q u i r e m e n t s . the h y d r o g r a p h i c cations w i l l 2.1 2.1.1  the  for  With t h i s i n m i n d ,  requirements and the f i n a l design  both  specifi-  be d e s c r i b e d .  S p e c i f i c a t i o n s From a Hydrographic  P o i n t of  View  A b s o l u t e Accuracy of L o c a l Height of Tide A c c u r a c y of the p r e s s u r e measurement was s p e c i f i e d  by the c o n t r a c t s u p p o r t i n g t h i s p r o j e c t  to be e q u i v a l e n t  t h r e e c e n t i m e t e r s o f water h e i g h t at t i d a l  to  frequencies.  Accuracy of e x i s t i n g s h o r e - b a s e d t i d e gauges i s near  three  c e n t i m e t e r s but t r a n s d u c e r s used f o r the o f f s h o r e gauge have a potential for better facilities  at d i u r n a l  i n h e r e n t accuracy than e x i s t i n g and h i g h e r f r e q u e n c i e s  (Caldwell,  S n o d g r a s s , and Wimbush 1 9 6 9 ) . Generally,  the accuracy s p e c i f i c a t i o n should be  determined by the g e o p h y s i c a l  background n o i s e of the o c e a n .  Even w i t h a " p e r f e c t " p r e d i c t i o n of t i d a l h e i g h t 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 n o i s e  5  added to the a c t u a l s i g n a l .  The p r e c e e d i n g statement i 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 of p r e d i c t i n g t i d a l  heights via conventional  Prediction is d i s t i n c t l y different l a t t e r c a s e , the n o i s e l e v e l and C a r t w r i g h t  respurposes  methods.  from a n a l y s i s where,  i t s e l f may be of i n t e r e s t  in the (Munk  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 : a c c u r a c y of the data need be no b e t t e r than the spectral noise l e v e l .  geophysical  S i n c e the n o i s e 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 r e q u e n c y .  As an approximate g u i d e l i n e  noise  l e v e l s near the c o a s t at s e m i - d i u r n a l f r e q u e n c i e s and lower are of the o r d e r of one c e n t i m e t e r and decrease w i t h i n c r e a s i n g frequency 2.1.2  (based on t e s t r e s u l t s  i n Chapter  VIII).  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* data w i l l  A net d r i f t  added to  i n f l u e n c e the very low frequency p o r t i o n of  spectrum most s t r o n g l y  and t h i s i s compounded by the  t h a t t i d a l components at those f r e q u e n c i e s are  The t r a n s d u c e r used with the o f f s h o r e gauge  a drift  t h a t s i g n i f i c a n t l y contaminates very low  components.  fact  exhibits  frequency  For the purposes of hydrography a d r i f t  r a t e 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 . low d r i f t  the  generally  small.  tidal  tidal  However,  cannot be a c h i e v e d by the o f f s h o r e gauge.  The  this  6 effective  value of d r i f t  i s determined in the s e c t i o n on data  analysi 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 ,  data can be d e f i n e d w i t h a sample i n t e r v a l  of s i x  However, w i t h 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 of the o c e a n , which r e s u l t s  interval  i n the  a Nyquist  response components,  background n o i s e , the sample  must be l e s s than s i x hours to a l l o w f o r  of the harmonics ( i n  hours.  i n harmonics of the t i d a l  and a d d i t i o n of the e v e r - p r e s e n t  tidal  sense)  determination  and, of c o u r s e , to  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 .  reduce  With most shore based  s t a t i o n s data i s logged on c h a r 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 t h a t l a b o u r c o s t s e f f e c t i v e l y  limit  the maximum sample r a t e . For the reasons d e s c r i b e d , hydrographers use a sample i n t e r v a l logging  instruments  the p r i o r i t i e s  of one hour.  to  becomes a q u e s t i o n of u s i n g 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 b a s i s the sample  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 , 1 0 . 0 minutes w i t h an i n t e r v a l providing  recorders,  are s h i f t e d so t h a t the economy r e f e r r e d  a v a i l a b l e storage in order  interval  With automatic data  i n c o r p o r a t i n g magnetic tape  above i s not s i g n i f i c a n t and i t all  normally  one year of  data.  of f i v e  minutes  7  2.1.4  O p e r a t i n g Depth  Requirements  The t i d e g a u g e 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 meters in depth. measure  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  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 between  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 2.1.5  130  I n s t a l l a t i o n Time  meters.  Requirements  T h e 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 year because 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 the w i n t e r . Recovery o f bottom mounted 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 time.  A convenient record  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 m o n t h a n d 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 2.2 2.2.1  this  time.  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 Required Resolution of Pressure 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  Measurement by t h e t i d e g a u g e 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 ( t ) +. g<p(t)> Z ( t ) Q  where  P  o^ ^ t  2.1  atmospheric pressure  =  <^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 order v a r i a t i o n i n depth r e s u l t s in  AP(Z) = < >gAZ  2:2  P  Given a s p e c i f i e d r e s o l u t i o n i n terms of d e p t h , e q u a t i o n d e f i n e s the r e q u i r e d r e s o l u t i o n i n the c o r r e s p o n d i n g measurement.  2.2  pressure  One c e n t i m e t e r has been chosen as a r e f e r e n c e  a c c u r a c y and i t  i s s t a n d a r d p r a c t i c e to i n c r e a s e the  precision  of the measurement to an o r d e r of magnitude beyond the reference.  A r e s o l u t i o n of one m i l l i m e t e r , which r e p r e s e n t s a  s t a b i l i t y of one p a r t i n 10  at 100 meters d e p t h , i s near the  l i m i t i n g s e l f - n o i s e of the t r a n s d u c e r used (Snodgrass taking  1968).  AZ = 10" m 3  2 g = 9 . 8 m/sec <p> = 1.03xl0 kg/m 3  The r e q u i r e d p r e s s u r e r e s o l u t i o n  3  is^  AP(Z) = 10 Pa 2.2.2  2.3  C o r r e s p o n d i n g R e s o l u t i o n s Necessary f o r C o r r e c t i o n s  to  Data Since bottom p r e s s u r e i s a f u n c t i o n of P as w e l l as d e p t h , c o r r e c t i o n s  for barometric  f l u c t u a t i o n s may be n e c e s s a r y . p r e s s u r e r e q u i r e d to c o r r e c t  Q  pressure  The r e s o l u t i o n of b a r o m e t r i c  the water p r e s s u r e 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 1  ?  inch  o  = 10 Pa  10 P a s c a l s ( P a ) 4 10 Newton meter" =• 0 . 1 0 m i l l i b a r s  2.4 9  =  0.0015 pounds  9  In p r a c t i c e , b a r o m e t r i c p r e s s u r e  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 r e a s o n s :  first,  the  weather  s t a t i o n i s u s u a l l y some d i s t a n c e from the t i d e gauge  location  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 i n a remote area where  weather s t a t i o n s r e c o r d p r e s s u r e at s i x hour i n t e r v a l s which not adequate f o r  interpolation  to the d e s i r e d r e s o l u t i o n .  can o n l y hope t h a t the v a r i a n c e i n t r o d u c e d by making to t i d a l  One  corrections  data i n t h i s manner i s small enough so t h a t the data i s  not a p p r e c i a b l y  biased.  The Hydrographer i s concerned w i t h water h e i g h t , relevant  is  parameter a f f e c t i n g marine t r a f f i c , which i s  the  calculated  from measured p r e s s u r e a c c o r d i n g to e q u a t i o n 2.1 ( w i t h removal of b a r o m e t r i c e f f e c t s ) .  Accuracy of the c o n v e r s i o n  dependent on knowledge of v a r i a t i o n s  i n depth averaged  d e n s i t y which are r e l a t e d to the d e s i r e d p r e s s u r e  At a depth of 100 meters and 10 P a s c a l s p r e s s u r e A  <p(t)) =  is  0.01  water  resolution  resolution,  kg  In terms of the oceanographic s p e c i f i c g r a v i t y parameter, t h i s becomes A (o^)  = 0.01  by  a, t  10 Not o n l y 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 o f t e n 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 i n o r d e r to a r r i v e the depth averaged v a l u e , density variations  <(a^)  •  D e t a i l e d knowledge  at  of  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  a m p l i t u d e data and, f o r t h i s r e a s o n , c o r r e c t i o n s are not normally a p p l i e d .  In h i g h l y  pressure-converted  a m p l i t u d e s are s i g n i f i c a n t l y l i m i t e d i n  a c c u r a c y at t i d a l  s t r a t i f i e d water near the c o a s t ,  frequencies.  The Oceanographer,  however, may be concerned w i t h  the "raw" p r e s s u r e r e c o r d s i n c e " t h e t i d a l p r e s s u r e  fluctuations  on the sea f l o o r r e f l e c t w e 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 t h a t of s u r f a c e e l e v a t i o n s "  (Filloux  1971).  Since the fundamental q u a l i t y being measured i s p r e s s u r e , r e f e r e n c e s to t i d a l h e i g h t s i n t h i s paper are conversions 2.2.3  from p r e s s u r e as d e f i n e d by e q u a t i o n 2 . 1 .  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 p r e s s u r e i s r e s t r i c t e d measurement of a b s o l u t e p r e s s u r e .  to  A b s o l u t e p r e s s u r e can be  d e t e c t e d d i r e c t l y w i t h an a b s o l u t e p r e s s u r e t r a n s d u c e r or an e q u i v a l e n t measurement can be made w i t h a d i f f e r e n t i a l ducer arranged to have one p o r t open to a r e f e r e n c e  trans-  pressure.  The r e s u l t s from both t e c h n i q u e s are comparable but the  11 a b s o l u t e t r a n s d u c e r i s much s i m p l e r to implement. t h i s work was s t a r t e d (1971) o n l y two a b s o l u t e  At the time  pressure  t r a n s d u c e r s were c o n s i d e r e d addquate f o r use as the s e n s o r . first,  a Hewlett-Packard quartz c r y s t a l  relatively  The  t r a n s d u c e r was  u n t r i e d at t h a t time and was a l s o f a i r l y  T h i s t r a n s d u c e r has s i n c e proved to have  expensive.  excellent  c h a r a c t e r i s t i c s f o r use as an a b y s s a l t i d e gauge ( I r i s h and Snodgrass 1972).  The s e c o n d , a V i b r o t r o n  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 w e l l known , i t relatively  is  i n e x p e n s i v e , a n d , of equal i m p o r t a n c e , the s t a f f  the I n s t i t u t e of Oceanography  have had e x p e r i e n c e w i t h  of  the  transducer. The V i b r o t r o n  c o n t a i n s a tungsten wire about one c e n t i -  meter i n l e n g t h s t r e t c h e d i n a magnetic f i e l d and e n c l o s e d i n a dry atmosphere at low p r e s s u r e .  One end of the w i r e  is  a t t a c h e d to a r i g i d frame w i t h the o t h e r end connected to a diaphragm.  Under p r e s s u r e , the diaphragm i n f l e c t s c a u s i n g  t e n s i o n of the w i r e and i t s n a t u r a l frequency of to d e c r e a s e .  vibration  With the w i r e 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  pressure.  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, R o l f e 1968, Snodgrass 1968, N. 0 . I. C. 1968, C a l d w e l l , S n o d g r a s s , 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 i n the time base of a t i d e  gauge m a n i f e s t s i t s e l f i n two ways: f o r a l i n e a r d r i f t  in  tidal  s p e c t r a l components are s h i f t e d i n the amount of  the  drift  r a t e and f o r a random e r r o r i n time the s p e c t r a are  blurred  (Godin 1973).  time,  These e f f e c t s are i m p o r t a n t when a  mechanical c l o c k i s used but are i n s i g n i f i c a n t when time i s d e r i v e d from a q u a r t z c r y s t a l  oscillator.  A crystal  r e f e r e n c e i s n e c e s s a r y to measure the output of Vibrotron  t r a n s d u c e r which r e l a t e s frequency  t h a t the q u a r t z c r y s t a l  time  the  to p r e s s u r e so  serves a dual p u r p o s e - t h a t of a master  c l o c k and t h a t of a p r e s s u r e r e f e r e n c e .  If  the  transducer  has a s e n s i t i v i t y of f i v e H e r t z 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 r a n s d u c e r output must be measured to a p r e c i s i o n of 0.005 H e r t z . c e n t e r frequency of 10 k i l o H e r t z ,  With a t r a n s d u c e r  the c r y s t a l  r e f e r e n c e must be  s t a b l e to w i t h i n 0 . 5 p a r t s per m i l l i o n (ppM). CMOS c r y s t a l  Bulova  provided  o s c i l l a t o r s w i t h 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  Ageing:  0 . 5 ppM/year  Temperature:  0 . 5 ppM/°c  turn-over temperature: Power: 3 ma @ 12 v ± 5%  -l°c  minute)  13 2.2.5  Recording System The r e c o r d e r  chosen f o r the t i d e gauge was a  Kennedy DSP 340 which i s an i n c r e m e n t a l d i g i t a l seven t r a c k s at 200 c h a r a c t e r s c o m p a t i b i l i t y , and r e q u i r e s tape at 12 v o l t s .  recorder  per i n c h , f e a t u r e s  with  IBM  f o u r ampere-hours per 300 f e e t  of  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  first  being p r e s s u r e  and  the second being a time so t h a t e a c h . p r e s s u r e measurement was a s s o c i a t e d w i t h a unique t i m e .  To f u r t h e r  of the data one channel was r e s e r v e d  Refer to  Although t h i s  in  figure  format  is  TIME  PRESSURE  CHANNEL  security  f o r a word address  order to d i s t i n g u i s h p r e s s u r e from t i m e . 2.1 f o r an o u t l i n e of the f o r m a t .  increase  DATA DATA DATA DATA DATA WORD ADDRESS PARITY SI  S2  S3  S4  S5  MUX STATE  F i g u r e 2.1 Format of Data W r i t t e n on Tape not e f f i c i e n t exhibit  i n terms of data s t o r a g e ,  the f o l l o w i n g a)  the t e c h n i q u e  does  features:  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 r e a l  time i f  c h a r a c t e r s are missed d u r i n g the read  o p e r a t i on. b) since i t s  The time tag word a c t s as a c o n t r o l  value i s p r e d i c t a b l e .  An o c c a s i o n a l  data b i t e r r o r i n the i n s t r u m e n t , can be u n i q u e l y faulty  component.  or tape  word which r e f l e c t s  reader  r e p a i r of a  S t a t i s t i c a l error information is  in pressure c)  persistant  i d e n t i f i e d and a l l o w s f o r e a r l y  p r o v i d e d by the c o n t r o l errors  recorder,  variable  also  the p r o b a b i l i t y  of  data.  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  i s achieved u s i n g the time tag word.  oscillator  The procedure  consists  s t a r t i n g the i n s t r u m e n t c l o c k u s i n g WWV r a d i o as a time reference,  n o t i n g the p r e c i s e time ( v i a WWV) of the  reading p r i o r  to shut down, and r e a d i n g the f i n a l  last  time word.  With t h i s technique the c a l i b r a t i o n can be a c c u r a t e to 0 . 5 ppM u s i n g a time base of o n l y one month. course, provides  o n l y an average frequency  within  The method, of  e r r o r over the  time base used. The f e a t u r e s  (a),  (b)  above i n d i c a t e an a n t i c i p a t e d  problem i n r e a d i n g the data a n d , as the s e c t i o n on data recovery w i l l  show, t h i s was the c a s e .  of  15  Chapter  III  SAMPLING CONSIDERATIONS 3.1  Tradeoffs  to C o n s i d e r i n Sampling Techniques  The V i b r o t r o n  t r a n s d u c e r has a t r a n s f e r  function  r e l a t i n g pressure- to frequency so t h a t the problem of measuring p r e s s u r e i s t r a n s f e r r e d to one of measuring frequency.  In p r a c t i c e , e i t h e r frequency or p e r i o d can be  sampled and t h e r e are t r a d e o f f s to c o n s i d e r w i t h regard to the two c h o i c e s .  C o n s i d e r the f o l l o w i n g : i f a s i g n a l  frequency F i s gated i n t o a counter f o r a time T the count  of total  is 3.1  n = FT The f i r s t o r d e r s e n s i t i v i t y of count (n) any v a r i a b l e (Z)  w i t h r e s p e c t to  is dn _ - 3 l + T I E dZ -3'Z 8Z  3.2  F  Only one of F,T  can be a l l o w e d to v a r y - r e s u l t i n g  i n two  p o s s i b i 1 i t i es  dn dZ  dT = F dZ  3.3  = T dZ^  3.4  1  E q u a t i o n 3 . 3 r e p r e s e n t s a p e r i o d measurement w h i l e e q u a t i o n 3.4 r e p r e s e n t s a frequency measurement, as i m p l i e d by the  16 s u b s c r i p t on 3.1.1  (n).  The Sampling C i r c u i t Before p u r s u i n g t h i s matter i t i s n e c e s s a r y  i n t r o d u c e the b a s i c measurement c i r c u i t used i n the gauge as d e p i c t e d i n f i g u r e  3.1.  to tide  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 c o u n t e r s are b i n a r y r i p p l e .  O p e r a t i o n of the sampling c i r c u i t  I  GZ)— 0 S  n I I I I I  Cl  R  i  •< — °  *\  D Q  —<  >  >1  G 3 «i—  i  m  1  F i g u r e 3.1 B a s i c 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 i n the  high s t a t e , c o u n t e r s C l , C 2 are held i n 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, i n the r e s e t mode, has i t s output stage (m) the low s t a t e .  When S goes l o w , the counter r e s e t s  removed and gate GI i s e n a b l e d . signal  F  9  will  in  are  The next r i s i n g edge of  set the f l i p - f l o p thus e n a b l i n g gates G2,G3 and  17 a l l o w i n g counters Cl ,C2 to accumulate p u l s e s on f a l l i n g edges of s i g n a l ml 2 "  F-.,F  2<  Finally,  counter C2 accumulates  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 F  2  will  r e s e t the f l i p - f l o p which  turn d i s a b l e s gates G2,G3 and stops the c o u n t . taken f o r c o u n t e r C2 to accumulate 2 ~^ c y c l e s m  9  c w h i l e the t o t a l  count in Cl  r  The sampler  described  features:  a) the c o n t r o l  S and the s i g n a l  need not be  s i n c e the sampler does t h i s  automatically.  b) the a p e r t u r e (n)  3.6  2  Compare e q u a t i o n 3 . 6 to e q u a t i o n 3 . 1 .  synchronized  3.5  is 1  two unique  is  2  n =F T  exhibits  The time  „m-l = 4  T  in  time T r e q u i r e d to take the sample 2  i s a p r e c i s e m u l t i p l e of the p e r i o d of  F. 2  S u b s t i t u t i o n of e q u a t i o n 3.5 i n t o 3.6 y i e l d s  F  2  m-l  n = p-!  If  the s i g n a l  F i s a c o n s t a n t c l o c k frequency 2  i s the V i b r o t r o n s i g n a l  3.7  (F ) and F. c  (F ) a frequency measurement  results  18 If  the r o l e s of F| and  are r e v e r s e d ,  a p e r i o d measurement  results:  n  where (k) 3.1.2  has r e p l a c e d  T  -f F  =  2  "-i  3.9  v  (m)  R e s o l v i n g the T r a d e o f f  Question  R e t u r n i n g to the q u e s t i o n of t r a d e o f f s frequency  and p e r i o d measurement, f i r s t  order  between sensitivities  of e q u a t i o n s 3 . 8 and 3.9 are  3.10  i i i i f . - ! _ ! ! .  dZ  c  " _ dZ d  F  T  The c o r r e s p o n d i n g a p e r t u r e  dZ  F  c  F  2 k  "  ]  2 V  A dZ d  3.11  times are  T  F  =  -j2  c  m _ 1  3.12  19 It  i s i n s t r u c t i v e to compare a p e r t u r e time f o r the two  t e c h n i q u e s at a common s e n s i t i v i t y :  let  then  dnp  dn j  dZ  dZ  3.14  ,m-k  3.15  Taking the r a t i o of a p e r t u r e times and u s i n g e q u a t i o n 3 . 1 5 yields  3.16  A s u i t a b l e v a l u e f o r the V i b r o t r o n and the c r y s t a l  frequency  (F ) i s 10 kHz  frequency (F ) i s near 500 kHz. c  Equation  3.16 shows t h a t T  F  = 5 0 Ty  3.17  T h e r e f o r e the t r a d e o f f to c o n s i d e r between frequency and p e r i o d measurement i s t h a t of d i f f e r e n c e s i n a p e r t u r e time and consequent e f f e c t s on the d a t a . For a t r a n s d u c e r s e n s i t i v i t y of f i v e H e r t z 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 a p e r t u r e time of f i v e minutes i s r e q u i r e d f o r frequency measurement. The c o r r e s p o n d i n g value f o r p e r i o d measurement at a t r a n s d u c e r frequency of 10 k i l o K e r t z i s a p p r o x i m a t e l y s i x s e c o n d s .  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 r a n s d u c e r frequency d u r i n g the a p e r t u r e 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 c o n t a i n e d i n the p r e s s u r e s i g n a l . e f f e c t i v e as a f i l t e r .  Frequency sampling i s c o n s i d e r a b l e more Conversely,  a longer aperture  reduces the maximum p o s s i b l e sample r a t e thereby  time  limiting  N y q u i s t frequency of the d a t a . It  was c o n s i d e r e d advantageous to a c h i e v e a high  frequency response w i t h the t i d e gauge r a t h e r than f i l t e r low-energy  high-frequency  p o r t i o n of the spectrum.  the  Both  p e r i o d and frequency measurement c o u l d have been i n c o r p o r a t e d w i t h the sampling c i r c u i t u s e d , but t h i s would c o m p l i c a t e o p e r a t i o n of the i n s t r u m e n t which d e t e r s from an aim of simplicity.  For these reasons the p e r i o d measurement  technique was c h o s e n . 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 i n a p e r i o d measurement mode: A n o i s e p u l s e coupled to the low l e v e l  Vibrotron  signal  can cause an increment to occur in counter C2, r e s u l t i n g a m o d i f i e d a p e r t u r e time of  in  21 Equation 3 . 9 p r o v i d e s  the m o d i f i e d sample n'y  F (2 " -D  ,  k  1  C  "  — T ~  T  The r e s u l t i n g e r r o r i n the sample i s An  T  = n-j- - n'y F _ _c F v  An^ = 50 c y c l e s Judicious  c h o i c e of l e a s t count s e n s i t i v i t y  c i r c u i t ensures  f o r the sampling  t h a t the change i n sample n^ from one r e a d i n g  to the next i s s i g n i f i c a n t l y  l e s s than 50 c y c l e s ,  i n d e t e c t i o n of e r r o r s of t h i s  type.  resulting  22  Chapter  IV  INVESTIGATION OF INSTRUMENTAL AND NATURAL DATA FILTERING The t o t a l wave spectrum of the ocean covers  ten decades of f r e q u e n c y ,  effectively  from the very long  t r a n s t i d a l waves to the very s h o r t  period c a p i l l a r y  The t i d e gauge d e s c r i b e d i n t h i s paper measures the p o r t i o n of the t o t a l  spectrum.  period waves. lower  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 critical  f o r proper  interpretation  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 determined i n p a r t by the "net" a p p l i e d to the d a t a . occur and t o g e t h e r 4.1  i n t h a t band i s  low-pass f i l t e r  Both i n s t r u m e n t a l and n a t u r a l  form a composite  F i l t e r i n g E f f e c t of S i g n a l  are used f o r sampling the t i d a l  Averaging  wave spectrum i s removed. will  now be examined.  techniques  s i g n a l , the a p e r t u r e  S i n c e the i n p u t s i g n a l  f o r the d u r a t i o n of the a p e r t u r e  filtering  filter.  Whether p e r i o d or frequency measurement  remains f i n i t e .  function  time  is effectively  "window",  averaged  a p o r t i o n of  The form of t h i s a v e r a g i n g  the  filter  23 f(t)  let  = pressure input signal f(t)  f (t) T  averaged f o r T seconds a t T  second i n t e r v a l s and sampled every T seconds. note t h a t  <T nT + f f(nT)  then  f(t)  4.1  dt  nT and  f  (t)  s ( t - nT) f (nT)  E  n = -oo  4.2  T  C o n s i d e r a s i n g l e F o u r i e r component of f ( t ) f (t) = f k  The i n t e g r a l  k  (nT) = S a ( ^ ) f (nT) s i n (x) O). T  f  (t) = Sa(-|-)  k  4.3  k  Sa(x)  where  Ul.T  = Sa(-|-) where  exp(j\ t )  yields f  and  k  f (nT) 6 ( t - nT)  E  k  f (t) 6 ( t ) k  4.4  T  « ( t ) = E 6 ( t - nT) n = -oo T  The F o u r i e r t r a n s f o r m of e q u a t i o n 4 . 4 i s F where and  T k  (.)  - - f s a ( ^ )  [F (. )  * £ convolution 2TT  k  k  * 6  operation  u  U)]  4.5  24 Summing over a l l F o u r i e r  components of f ( t )  F («o) = | s a ( ^ )  yields  [F(co) * «  (oo)]  4.6  o  The spectrum of the sampled but non-averaged i n p u t has the form ( L a t h i  signal  1968 page 90)  F. (to) = \  [F(to) * 6  I  OJ  5  U)]  4.7  0  Comparison o f e q u a t i o n s 4 . 6 and 4 . 7 show t h a t the spectrum of the i n p u t s i g n a l  has been m o d i f i e d by the sampling  S a ( - ^ ) which e f f e c t i v e l y following  function  a c t s as a l o w - p a s s f i l t e r  w i t h the  characteristics: a) The envelope o f S a ( - ^ )  r o l l s o f f with a f i r s t  order s l o p e f o r | OJ | > ^ b) Sa(*y) goes to zero at u> = n = ±1, ± 2 , . . . c) Isaty )! has a l o c a l maximum at = ^ 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 1  u  ( 2 n  ) T r  order l o w - p a s s f i l t e r w i t h a b r e a k p o i n t at u = — . The high frequency dominated by w i n d - d r i v e n order o f one meter.  p o r t i o n of the wave spectrum i s  swell with t y p i c a l  T h i s data i s a l i a s e d to lower  u n l e s s i t i s removed by f i l t e r i n g . a frequency  averaging f i l t e r  frequency  With the s w e l l  frequencies occuping  band of about 200 to 700 c y c l e s per h o u r ,  millimeter resolution  of s w e l l  a m p l i t u d e s i n the  and one  i n the p r e s s u r e measurement, the  provides  f o r three to ten d e c i b e l s  attenuation  f o r p e r i o d measurement and 35 to 45 d e c i b e l s f o r measurement.  25 4.2  Natural  4.2.1  Filtering  Filtering The  in  Action  the  of  ocean water  Deep W a t e r  column behaves  to passage of w i n d - g e n e r a t e d wave p r e s s u r e and wave is the  fluctuations  frequency.  pressure filter  sea f l o o r  so t h a t function  to  the o c e a n .  The  is  amplitude to d e p t h  variable  one t h a t  the  via  m e a s u r e d by t h e transfer  and f r e q u e n c y  filter  surface depth  tide  function  to  r e l a t e s wave p r e s s u r e just  transfer  Bernoulli's  the  of  instrument  below the  function is  transfer  (w) i s  Using  function  expressed  in  gauge describe on  the  surface  from  classical  Kinsman 1965 page 1 4 1 ) .  approximation^, (h)  Attenuation  pressure  Development of  (see  as a low pass  increases with  (unattenuated)  here  waves.  a convenient  Navi e r - S t o k e s e q u a t i o n repeated  Ocean  the  and i s  the  of  not  small  relating  gain  parametric  f o r m as H(u>,k) 2 where and  k  = [cosh(kh)] = gk 2jT  x  -1  4.8 4.9  [tanh(kh)] = r a d i a n wave  number  X = wavelength  F o r s m a l l a m p l i t u d e s , wave h e i g h t wave l e n g t h . F o r most g r a v i t y waves t h i s i s approximation.  i s much l e s s a good  than  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 l o p e of about 300 d e c i b e l s per decade a t 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 1  1  V  —  WIND-GENERATED SWELL  1  \ \o \-o  \ -A  \l  40  \o  -  \o  r  -  \ °  V \3  10'  I0  lO  2  10  3  FREQUENCY cy/hr  i  1  F i g u r e 4.1 A t t e n u a t i o n of the P r e s s u r e E f f e c t of S u r f a c e Waves as Measured on the Sea F l o o r as a f u n c t i o n of Frequency and Depth depth of 1000 meters most of the energy from w i n d - g e n e r a t e d swell  i s removed w h i l e a t 10 meters much of the wave energy  remains. 4.2.2  A t t e n u a t i o n of Swell 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 w a t e r ,  r e s u l t i n g i n 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 t h a t 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 a t t e n u a t e d w h i l e l o n g - p e r i o d waves are s t i l l several  detectable  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 fluctuations  generated s w e l l ,  local  barometric  and winds may cause waves i n sea i c e (Hunkins  1962).  FREQUENCY  cy/hr  F i g u r e 4.2 G e n e r a l i z e d Amplitude Spectrum of Waves on the A r c t i c Ocean ( a f t e r Hunkins 1962) w i t h the E f f e c t of Depth F i l t e r i n g I n c l u d e d The amplitudes of these waves are q u i t e s m a l l , the o r d e r one c e n t i m e t e r or l e s s ,  so t h a t c o n t a m i n a t i o n of t i d a l  is barely s i g n i f i c a n t .  F i g u r e 4.2 shows the a m p l i t u d e  of  data  spectrum of measured waves i n the A r c t i c Ocean (Hunkins 1962) w i t h the e f f e c t s of depth f i l t e r i n g With a sample i n t e r v a l t i d e gauge r e s u l t s w i l l  overlap  by one decade which may p r o v i d e  included.  of f i v e m i n u t e s ,  offshore  the spectrum of f i g u r e f o r an e x t e n s i o n of  g e n e r a l i z e d spectrum down to t i d a l  frequencies.  the  4.2  28  Chapter V ELECTRONIC AND MECHNICAL DESIGN 5.1  Electronic  Design  Compl e m e n t a r y - m e t a l - o x i d e - s e m i conductor (CMOS)  logic  was chosen f o r the t i d e gauge f o r i t s very low power requirements.  Q u i e s c e n t power d i s s i p a t i o n i s t y p i c a l l y  orders of magnitude below t h a t of comparable b i p o l a r w h i l e dynamic power consumption i s a f u n c t i o n of and l o a d c a p a c i t a n c e . of n o n - c r i t i c a l  three  circuits,  frequency  Other f e a t u r e s of CMOS l i e i n areas  supply v o l t a g e s , high n o i s e immunity, medium  speed c a p a b i l i t i e s , and high  fan-out.  Complete c i r c u i t diagrams are p r o v i d e d i n Appendix 1 and some design f e a t u r e s of the c i r c u i t s are presented below. CONTROL and SAMPLING CIRCUITS: rate, write  frequency,  Timing o p t i o n s such as sample  r e c o r d gap s e l e c t , and  sensitivity  s e l e c t are on the c i r c u i t boards i n the form of w i r e  jumpers  s i n c e these s e t t i n g s are fundamental to o p e r a t i o n of the i n s t r u m e n t and are not n o r m a l l y changed once c o n n e c t e d . All  tape r e c o r d e r c o n t r o l s are s u p e r v i s e d by the  master t i m i n g l i n e i n an asynchronous manner to ensure r e c o v e r y 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 s a m p l i n g interval.  29 MANUAL CONTROLS:  The master c o n t r o l  an aim f o r s i m p l i c i t y .  Instrument  panel was designed w i t h  operation 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 r e s e t / r u n c o n t r o l count-down c i r c u i t s . control  for clock  While i n the r e s e t mode, the  reset/run  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 r e c o r d e r  Other manual c o n t r o l s  i n c l u d e push buttons f o r :  EOF g a p s , s l e w i n g the tape (and EOR g a p ) , f o r the sample i n d i c a t o r .  circuits.  generation  and an enable  the tape c a r t r i d g e  control  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 r e c o r d e r i n t e r l o c k l e v e r fixes  of  in p l a c e .  which  A l l s w i t c h e s are  connected to ground i n t h e i r normal o p e r a t i n g s t a t e s and are shunted w i t h a r e s i s t o r to ensure a ground c o n n e c t i o n i n case of minor s w i t c h c o n t a c t SIGNAL CONDITIONING:  corrosion.  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 r a n s c o n d u c t a n c e a m p l i f i e r (OTA) an open l o o p mode as a comparator.  operating  The output of the  i s passed through one s i d e of the OTA.  The r e f e r e n c e  of the a m p l i f i e r i s a l s o used to clamp the a - c output.  Vibrotron  s i g n a l can be e x t r a c t e d i n the presence  input  In t h i s way the a - c component of the  i n the r e f e r e n c e l e v e l .  of  T h i s 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 .  Hysteresis  i s p r o v i d e d by a l o w - p a s s f i l t e r a t t e n u a t i n g the i n p u t phase s h i f t i n g i t 90 d e g r e e s , and adding i t r e f e r e n c e 1 evel .  Vibrotron  coupled  Vibrotron  considerable d r i f t  in  to the  d-c  signal,  30 POWER SUPPLY and REGULATION:  Power i s p r o v i d e d by  hard-topped lead acid b a t t e r i e s acid)  i n an o i l  specific-gravity  bath which i s open to ambient p r e s s u r e  a neoprene diaphragm. of three c e l l s ,  ( w i t h low  three  One b a t t e r y  thus p r o v i d i n g  s u p p l i e s at 12 and 18 v o l t s  via  i s d i v i d e d i n t o two s e t s  two independent  voltage  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 s u p p l y .  The 12 v o l t supply  provides  power f o r the l o g i c and tape r e c o r d e r w h i l e the 18 v o l t s u p p l i e s the v o l t a g e r e g u l a t o r s .  level  C u r r e n t d r a i n on the 18 v o l t  supply was e i g h t mi 11iamperes and on the 12 v o l t s u p p l y , than one m i l l i a m p e r e .  A p p r o x i m a t e l y 70 ampere-hours  r e q u i r e d f o r one y e a r ' s o p e r a t i o n .  The v o l t a g e  less  is  regulators  share a temperature-compensated zener r e f e r e n c e diode such t h a t the net e f f e c t of v o l t a g e changes on the 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 specification.  crystal  stability  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  w o r s t - c a s e i n p u t v o l t a g e changes i s an o r d e r 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 regulator'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  is  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 l a y o u t 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 p r e s s u r e housing dimensions  were 107 c e n t i m e t e r s l o n g by 28 c e n t i m e t e r s i n diameter and c o n s i s t e d of two compartments.  The s m a l l e r primary chamber  31 c o n t a i n e d the V i b r o t r o n  with a m p l i f i e r , signal  conditioner,  and diode i s o l a t o r s  the power s u p p l y .  secondary  for  The  chamber c o n t a i n e d the e l e c t r o n i c s w i t h tape r e c o r d e r i s o l a t e d from the primary by a bulkhead i n o r d e r the system from e f f e c t s of a t r a n s d u c e r penetrator  to  or b a t t e r y  and was protect  cable  leak.  A fiberglass  box of dimensions 57 c e n t i m e t e r s  long by  31 c e n t i m e t e r s wide by 30 c e n t i m e t e r s high c o n t a i n e d the immersed b a t t e r i e s .  The l i d df the b a t t e r y  a neoprene diaphragm under a p o l y v i n y l containing ventilation pressure  to the o i l  oil  case c o n s i s t e d  chloride  of  plate  holes to a l l o w t r a n s m i s s i o n of ambient  bath.  The support frame was c o n s t r u c t e d of welded angle i r o n and was 122 c e n t i m e t e r s by 152 c e n t i m e t e r s . were p r o v i d e d sling.  i n each c o r n e r  Lifting  f o r attachment of a s t e e l  The complete u n i t had a weight e q u i v a l e n t  k i l o g r a m s in a i r and 150 k i l o g r a m s in  cable  to 300  water.  Components of the frame and housing i n c o n t a c t made from m a t e r i a l s of s i m i l a r l e v e l activity  to l i m i t chemical c o r r o s i o n .  were  i n the e l e c t r o c h e m i c a l  s e r i e s to minimize e f f e c t s of G a l v a n i c  In a d d i t i o n , the s t e e l p r e s s u r e  lugs  corrosion.  housing was coated w i t h epoxy  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 r e s u l t i n g i n f l a k i n g of the p r o t e c t i v e  from t h a t of coat.  steel-  F i g u r e 5.1  Exploded View of the C o n t i n e n t a l S h e l f Tide Gauge  33  Chapter  VI  CALIBRATION PROCEDURES AND RESULTS 6.1  Calibration  Procedure  The p r e s s u r e s e n s i n g element of the t i d e c o n s i s t s of a V i b r o t r o n  t r a n s d u c e r and i t s  gauge  associated  a m p l i f i e r which t o g e t h e r have a t r a n s f e r f u n c t i o n 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 ,  relating  however,  is  a l s o s e n s i t i v e to ambient temperature w h i l e the a m p l i f i e r exhibits  some v o l t a g e s e n s i t i v i t y .  When making  r e s o l u t i o n p r e s s u r e measurements the secondary  high sensitivities  become s i g n i f i c a n t and some knowledge of them i s  required.  The p r e s s u r e 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 c o n s t a n t v o l t a g e w i t h a monitored r e f e r e n c e source and a p p r o x i m a t e l y c o n s t a n t temperature w i t h a l a r g e water b a t h . The p r e s s u r e source was a dead-weight t e s t e r w i t h a copper tube to t r a n s m i t p r e s s u r e to the t r a n s d u c e r which was c o n t a i n e d i n a small w a t e r - t i g h t water b a t h .  housing immersed i n  the  The bath was c o o l e d w i t h i c e and repeated  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.  pressure  The thermal  time c o n s t a n t of the water bath was about 10 hours so t h a t  the  temperature changed by l e s s than 0 . 5 degrees C e l s i u s d u r i n g a calibration.  Using a c a l i b r a t e d frequency c o u n t e r ,  readings  were taken f o r both i n c r e a s i n g and d e c r e a s i n g p r e s s u r e equal time i n t e r v a l s .  at  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 a v e r a g i n g the and f a l l i n g c u r v e s .  The time r e q u i r e d f o r a s i n g l e  rising  calibration  was v a r i e d and t h i s al1 owed removal of temperature dependence i n 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 d u r i n g the c a l i b r a t i o n . A d e t a i l e d v o l t a g e c a l i b r a t i o n was performed at atmospheric p r e s s u r e and gross c a l i b r a t i o n s were w i t h the p r e s s u r e c a l i b r a t i o n s .  An independent  included temperature  c a l i b r a t i o n was done at atmospheric p r e s s u r e by c o o l i n g an i n s u l a t e d t r a n s d u c e r 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 . B a r o m e t r i c p r e s s u r e was monitored d u r i n g a l l  calibrations  i n o r d e r to p r o v i d e an a b s o l u t e r e f e r e n c e f o r the 6.2  data.  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 t h r e e  Vibrotron  t r a n s d u c e r s of which one had a maximum p r e s s u r e of 70x10 Pascals  (10^ pounds per square inch)  maximum of 3.5x10  and the o t h e r s had a  P a s c a l s (500 pounds per square  inch).  The t r a n s d u c e r s are r e f e r r e d to in what f o l l o w s by a combination of the m a n u f a c t u r e r ' s i n i t i a l s and the serial  number so t h a t the high p r e s s u r e V i b r o t r o n  device was  designed UC173 w i t h the o t h e r s a s s i g n e d BJ5811 and UC92, where UC r e f e r s B.J.  to United C o n t r o l  Electronics.  C o r p o r a t i o n and BJ r e f e r s  to  Most p r e s s u r e s are expressed in terms of  e q u i v a l e n t water depth to p r o v i d e  a basis for comparison.  35  6.2.1  V o l t a g e and Temperature 51  Calibrations  The v o l t a g e 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 v a l u e s f o r the two a m p l i f i e r s were near - 1 . 0 c e n t i m e t e r per v o l t at 12 v o l t s  and adequate o p e r a t i o n was a c h i e v e d over  a supply range of 10 to 20 v o l t s . o p e r a t i n g p r e s s u r e was n o t i c e d .  Only a s l i g h t dependence on The net e f f e c t of  battery  v o l t a g e 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 . Cross-plotting temperature s e n s i t i v i t y It  was f e l t ,  however,  temperature and p r e s s u r e data as a f u n c t i o n of o p e r a t i n g  t h a t t h i s technique d i d not  provided  pressure. provide  r e l i a b l e data s i n c e repeated a p p l i c a t i o n of maximum p r e s s u r e c y c l e s r e s u l t e d i n 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 r e q u i r e d a number of hours to d i s s a p p e a r , 1  tended to d i s t o r t sensitivity.  the p r e s s u r e dependency of  temperature  Work by o t h e r s has i n d i c a t e d t h a t changes  temperature s e n s i t i v i t y the f u l l  These o f f s e t s  in  are g e n e r a l l y l e s s than 10 p e r c e n t over 2  s c a l e p r e s s u r e range  .  Temperature  sensitivity  v a r i e d w i t h the p a r t i c u l a r t r a n s d u c e r but was c o n s i s t a n t f o r an individual  device.  pressure, v i r t u a l l y  The measured s e n s i t i v i t i e s at atmospheric independent of the a m p l i f i e r u s e d , were as  fol1ows:  H y s t e r e s i s was t y p i c a l 1 y 0.02 per Snodgrass ( p e r s o n a l  cent.  communication).  36 337.0 cm °C 23.1  cm  + 19.4 cm  (UC173)  (UC92)  (BJ5811)  The t i d e gauge i s n o r m a l l y used i n c o n j u n c t i o n w i t h a c u r r e n t meter which a l s o measures temperature to w i t h i n 0 . 0 3 degrees Celsius.  Using the S* v a l u e s and temperature data a l l o w s  c o r r e c t i o n of t i d a l data to a p p r o x i m a t e l y 0 . 5 c e n t i m e t e r UC92 and BJ5811.  The a c c u r a c y of UC173 a f t e r  for  temperature  c o r r e c t i o n i s o n l y 10 c e n t i m e t e r s and f o r t h i s reason UC173 was not used i n 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 P r e s s u r e C a l i b r a t i o n Data Structural  a n a l y s i s of the V i b r o t r o n  transducer  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 (P)  to frequency  (F ) v  pressure  s h o u l d be a polynomial of the form  ( L e f c o r t 1968) P= where a , c are c o n s t a n t s f i t t e d to the c a l i b r a t i o n d a t a . was decided to t e s t t h i s theory by f i t t i n g f i v e p o l y n o m i a l s to the d a t a .  It  different  A measure of accuracy of the f i t was  p r o v i d e d by s t a n d a r d d e v i a t i o n of d i f f e r e n c e s  between  37 e x p e r i m e n t a l p r e s s u r e r e a d i n g s 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 m e r i t  r e p r e s e n t i n g c o m p l e x i t y of  the  polynomial was p r o v i d e d by the product of number of c o n s t a n t s i n an e q u a t i o n w i t h o r d e r of the p o l y n o m i a l .  The  test  p o l y n o m i a l s and a s s o c i a t e d f i g u r e s of m e r i t (FoM) were as follows: FoM  Test Equation  2  P = a + bF  6.1  4  P = a+  cF  v  6  P = a + bF + c F  v  12  P = a + bF + c F  y  20  P = a + bF + c F  y  v  y  v  y  2  6.2  2  6.3  2  + dF  y  2  + dF  y  6.4  3  3  + eF  v  6.5  4  F i g u r e 6.1 i l l u s t r a t e s the r e s u l t s w i t h s t a n d a r d  deviation  ( n o r m a l i z e d w i t h r e s p e c t to maximum p r e s s u r e to which the c a l i b r a t i o n s were c a r r i e d )  plotted against r e l a t i v e figure  of  meri t . A s t a t i s t i c a l a c c u r a c y 1 i m i t f o r the c a l i b r a t i o n data i s r e p r e s e n t e d by the l e v e l  of the p l a t e a u a c h i e v e d f o r each  of the curves i n 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 " F i g u r e of m e r i t " i n t h i s c o n t e x t 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 .  than  38 a b s o l u t e a c c u r a c y of the t r a n s d u c e r or dead-weight  tester.  The " b e s t " c a l i b r a t i o n curve has a low s t a n d a r d 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  figure  10 O  Q  I-  LU  <  ^  > LU  N  I L BJ58II  UC92  UCI73  <  1110 ' h ^  rc  CO  10  0  •20  0  20  FIGURE OF MERIT Figure 6.1 Standard D e v i a t i o n 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 m e r i t f o r the opitimum e q u a t i o n appears at the elbow of curves of f i g u r e  the  6.1 and the c o r r e s p o n d i n g optimum e q u a t i o n s  f o r each of the transducers a r e : e q u a t i o n 6 . 3 f o r BJ5811, UC92 4  and e q u a t i o n 6 . 2 f o r UC173 . The maximum c a l i b r a t i o n p r e s s u r e f o r UC173 was o n l y 20 per cent of r a t e d p r e s s u r e . For BJ5811 and UC92 the c o r r e s p o n d i n g values were 110 per cent and 100 per cent respecti vely.  39 A summary of c o n s t a n t s f o r the c a l i b r a t i o n e q u a t i o n s provided  in t a b l e  is  I. Table I  C a l i b r a t i o n Constants f o r V i b r o t r o n  Transducer  Transducers  Equation 6 .3  Equation 6.2 a  c  a  b  c  kPa  kPa (kHz)  kPa  kPa kHz  kPa (kHz)  2  2  UC92  15083.0  -118.815  13869.9  232.238  -129.875  BJ5811  15251.3  -874.483  14676.9  298.197  -912.963  UC1 73  84965.5  -268.445  Accuracy of c a l c u l a t e d t i d a l  heights  c a l i b r a t i o n equation i s s i g n i f i c a n t l y of c a l i b r a t i o n p o l y n o m i a l .  dependent on the c h o i c e  R e p r e s e n t i n g a change i n  amplitude as a measured frequency quiescent operating point  from the  excursion  tidal  ( A F ) from a  (F ) , . t h e d i f f e r e n c e  v  ( e ) in  excursion  p r e s s u r e s as c a l c u l a t e d from e q u a t i o n s 6 . 2 and 6 . 3 i s  e  E  =  A  P  ^ b  6.36  f  3  A  +  P  6.2 2(c  6  i  3  -c  6  -  2  )F ]AF V  V  For a t i d a l a m p l i t u d e of three m e t e r s , the d i f f e r e n c e ( e ) can be as l a r g e as two c e n t i m e t e r s 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  from the secure e n v i r o n s sometimes hazardous  must o i l t i m a t e l y be removed  of the l a b o r a t o r y  real world.  and p l a c e d i n  In s i t u t e s t s of a t i d e  such as the one d e s c r i b e d here r e q u i r e s  a considerable  i n the form of l o g i s t i c s , p e r s o n n e l , and t i m e .  i n s t r u m e n t performance s i n c e t i d a l  A test  harmonic a n a l y s i s  a r e c o r d l e n g t h of one l u n a r month f o r proper  7.1.1  gauge effort  period  of one month was c o n s i d e r e d adequate f o r an e s t i m a t i o n  of dominant t i d a l  the  of  requires  separation  components.  Choosing a Test Region The f o l l o w i n g f a c t o r s were c o n s i d e r e d i n the  of l o c a t i o n f o r f i e l d  trials:  a) A t e m p e r a t u r e - r e c o r d i n g available,  c u r r e n t meter was not  thus the prime q u a l i f i c a t i o n f o r the t e s t  was t h a t of r e l a t i v e l y  choice  constant  location  temperature.  b) Reasonably a c c u r a t e b a r o m e t r i c data f o r the  region  had to be a v a i l a b l e . c) Some knowledge of expected mean water v a r i a t i o n s was r e q u i r e d f o r proper  interpretation  density of  results.  41 d) The l o c a t i o n had to be near enough to the laboratory  to permit o v e r n i g h t r e p a i r s , i f  r e q u i r e d , and to  a l l o w f o r f r e q u e n t r e a d i n g s of the water h e i g h t  staff.  Upper Howe Sound and Saanich i n l e t were c o n s i d e r e d as p o s s i b l e l o c a t i o n s s i n c e both are f i o r d - t y p e  estuaries  having deep water and are p r o t e c t e d from e x t e r n a l i n f l u e n c e s by a s i l l .  Saanich i n l e t had fewer  v a r i a t i o n s and more a c c u r a t e  1  density  b a r o m e t r i c records  Howe Sound but Saanich I n l e t , l o c a t e d i n south  temperature  than upper 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 was l o c a t e d on the mainland at the U n i v e r s i t y . Sound was chosen as the main t e s t 7.1.2  I n s t a l l a t i o n and Recovery  which  Upper Howe  site. Techniques  The two i n s t r u m e n t housings were designed to w i t h s t a n d a maximum p r e s s u r e of IO' 1000 m e t e r s .  7  P a s c a l s , e q u i v a l e n t to a depth of  P r i o r to complete i n s t r u m e n t t e s t s , the  housings  were p r e s s u r e t e s t e d to a depth of 550 meters f o r a p e r i o d of two h o u r s . The procedure f o l l o w e d 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 by the Hydrographic  adopted  S e r v i c e f o r i n s t a l l a t i o n of c u r r e n t m e t e r s .  F i g u r e 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 f o r the t e s t s e r i e s i n Howe Sound.  The t i d e gauge was lowered  "More a c c u r a t e " 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 , buoy.  For c o n t i n e n t a l  f o l l o w e d by the a n c h o r , then the 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  s u b s u r f a c e c u r r e n t meter was suspended above the t i d e  gauge,  the buoy was a b s e n t , and an a c o u s t i c r e l e a s e d e v i c e was p l a c e d between the ground l i n e and the a n c h o r . or the a c o u s t i c r e l e a s e f a i l s  If  the buoy i s  to o p e r a t e , the ground  lost  line  serves as a secondary r e c o v e r y system.  F i g u r e 7.1 T y p i c a l Test S e r i e s  Tide Gauge I n s t a l l a t i o n f o r Howe Sound  No problems were encountered w i t h 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 p r e s s u r e  housing  (150 k i l o g r a m s ) proved somewhat d i f f i c u l t to handle d u r i n g service periods.  The s i z e and mass o f the complete i n s t r u m e n t  required that a l l  s h i p b o a r d d i s a s s e m b l y and assembly had to  be done o u t d o o r s .  7.2  Other F i e l d T e s t s R e l a t e d 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  t i d e gauge, the b a s i c concepts of the i n s t r u m e n t were by breadboarding a s h a l l o w - w a t e r v e r s i o n of the gauge.  The temporary model c o n s i s t e d of a low  (2x10^ P a s c a l s ) V i b r o t r o n  shelf  tested  offshore pressure  t r a n s d u c e r and a m p l i f i e r mounted i n  a small p r e s s u r e housing and connected to the e l e c t r o n i c s with a c a b l e .  The output frequency o f the V i b r o t r o n was  sampled, converted to an analogue v o l t a g e and r e c o r d e d on chart paper.  An e i g h 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 C o l u m b i a .  Comparisons between the  permanent f l o a t gauge and s h a l l o w - w a t e r gauge p r o v i d e d 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  offshore  t i d e gauge a second v e r s i o n of the s h a l l o w - w a t e r gauge u s i n g the same t r a n s d u c e r was breadboarded f o r the purpose  of  measuring s e i c h e s in San Juan harbour at P o r t Renfrew,  British  2  Columbia .  Two sampling c i r c u i t s were i n c o r p o r a t e d in the  wave gauge, both of which operated in a c o n t i n u o u s mode. One sampler measured the V i b r o t r o n  frequency at a low  r e p e t i t i o n r a t e of 0.05 H e r t z w h i l e the o t h e r measured p e r i o d at a high r a t e of one H e r t z . split  The output of each sampler was  i n t o two o v e r l a p p i n g e i g h t b i t numbers thus 2  Instrument d e t a i l and data w i l l Lemon's MSc t h e s i s (to be completed)  providing  be p r e s e n t e d i n D.  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 yielding  the t o t a l wave spectrum and the slow sampler  providing  a low passed v e r s i o n of the spectrum.  The  four  samples were p l a c e d i n h o l d i n g r e g i s t e r s , converted  to analogue  voltages,  recorder.  and s t o r e d by a f r e q u e n c y - m o d u l a t e d  tape  The tapes were then demodulated i n the l a b o r a t o r y e x i s t i n g equipment, d i g i t i z e d , The r e c o r d i n g  with  and s t o r e d on n i n e - t r a c k  scheme was somewhat i n d i r e c t  tape.  but r e s u l t e d  in  c o m p a t i b i l i t y w i t h 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 , August 1973 a n d ' i n F e b r u r a r y  1974.  Initial  results  in  were  e n c o u r a g i n g , with wave h e i g h t s of l e s s than one m i l l i m e t e r d e t e c t e d as w e l l as t i d a l waves of f o u r meters representing  an e f f e c t i v e  dynamic measurement range i n  of f o u r decades c o v e r i n g n e a r l y f i v e decades of 7.3  Recovery of O f f s h o r e  height,  Tidal  frequency.  Data  The sampling t e c h n i q u e , data format on t a p e , transducer  r e s p o n s e , and necessary data c o r r e c t i o n s  to y i e l d a f o r m i d a b l e problem of data r e d u c t i o n arrive  at a time s e r i e s of t i d a l  were w r i t t e n functional reference.  excess  heights.  to process the data i n l o g i c a l  nonlinear  combined  in order  A number of steps.  to  programs  The  c o n t e n t s of the programs are d e s c r i b e d below  for  45  7TC0N:  Read the s e v e n ^ t r a c k i instrument t a p e , - 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 t a p e .  T h i s program a l s o  p r o v i d e d output of any d e s i r e d r e c o r d i n decimal on a l i n e printer.  W r i t t e n in assembly language f o r the PDP-12 at the 3 I n s t i t u t e of Oceanography . TRANS:  Provided  WRPRND:  diagnostic  i n f o r m a t i o n on recorded time d a t a .  Removed f u l l - s c a l e wraparounds  i n sampled data and  r e s t o r e d most s i g n i f i c a n t p o r t i o n of s a m p l e s , which was not recorded. DEGLCH:  Provided error  diagnostics  on sampled d a t a .  Error  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 n e x t .  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 . to r e c o v e r  Failure  r e s u l t e d i n p r e s e n t r e a d i n g being s e t equal  to  p r e v i o u s sample. CONVRT:  Converted sampled data to V i b r o t r o n  sampler t r a n s f e r f u n c t i o n .  frequency  via  C o r r e c t e d frequency values  for  time s e r i e s temperature s e n s i t i v i t y .  Converted  frequency  values to p r e s s u r e u s i n g the t r a n s d u c e r c a l i b r a t i o n e q u a t i o n . BAROPR:  Corrected pressure record for barometric  time s e r i e s . o  pressure  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  7TC0N was w r i t t e n by M. M i l l a r , then s t a f f at the I n s t i t u e of Oceanography.  programmer  46 pressure time  record.  Converted  Produced  a tidal  output  sample  linear  interpolations  also  rate,  incorporated  word  for  each  technique TRANS  less  than  plots  of  of  the  had  per  tidal  height  signal,  number  detected  by  error  detected  by  of  circuit from  data  channel  resulting  to  thus  in  to  proved  to  that  rate  a n d TRANS  was  DEGLCH  also  DEGLCH  but  the  removing digital  data  in  at  cause  to  and  rate  program  detection  the  rate  of  Vibrotron  of  noise  the  1.5  per  cent.  operation  of  not  of  to  0.3  pressure was  useful  analogue  a read  a rate  time-tag  The  circuits  the  a  a source  error  occurred  precise  routines.  error  of  was  a very  led  relocation  reflected  be  h a d an  tape c h a r a c t e r s missed during  7TC0N  program  record  that  time,  Performed  performance.  program  the  samples.  analysis  component  led  start  the  information  The  desired  This  instrument  cent.  coupled  any  output  measurement  sampled data  been  Vibrotron  This  to  record.  a separate  diagnostic  signal-conditioning which  many o f  multiplexer  0.1  at  of  input  optimizing  provided  a faulty  on  pressure  for  record  and number  into  Inclusion  The  record  series.  GENREC:  of  pressure  per  data  as cent.  as  determined.  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 p r o t o t y p e s  underwent  f i e l d t r i a l s from June 2 6 , 1973 to September 1 8 , 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 i b r o t r o n UC92.  transducer  Both i n s t a l l a t i o n s o c c u r r e d near B r i t a n n i a B e a c h ,  B r i t i s h C o l u m b i a , l o c a t e d on upper Howe Sound. series,  d e s i g n a t e d HOI,  The  first  s t a r t e d at 1 2 : 2 6 : 1 5 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. 146.95 m e t e r s .  Mean i n s t r u m e n t depth was  The second s e r i e s , H02, was at the same  p o s i t i o n i n a depth of 173.19 m e t e r s , s t a r t e d at 1 2 : 4 8 : 4 5 PST August 7, and stopped at 2 3 : 2 8 : 3 5 PST September 1 3 . 8.1  provides  Figure  a map of the t e s t r e g i o n w h i l e 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 Barometric c o r r e c t i o n s records at Vancouver  f o r both s e r i e s was 0.625 m i n u t e s .  to the data were d e r i v e d from weather  International  k i l o m e t e r s from the t e s t s i t e .  Airport,  a d i s t a n c e of 45  A i r p r e s s u r e 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 intermediate values.  Gross temperature c o r r e c t i o n s  were  d e r i v e d from oceanographic s t a t i o n Howe 4 . 5 monthly data records.  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,  for  F i g u r e 8.1  Upper Howe Sound Showing L o c a t i o n of Test S i t e  Figure 8.2  Tidal  Time S e r i e s Used f o r Data A n a l y s i s  50 and September temperature r e a d i n g s Maximum temperature v a r i a t i o n was 0.1 degrees  for intermediate  values.  f o r the three monthly  readings  Celsuis.  Time dependent d e n s i t y c o r r e c t i o n s ,  useful  for  shore  based water h e i g h t c o m p a r i s o n s , were not a p p l i e d because of i n s u f f i c i e n t data.  Density  values a v a i l a b l e from the  monthly samples at S t a t i o n Howe 4 . 5 i n d i c a t e d the of p r e s s u r e  to depth c o n v e r s i o n  three  possibility  d i s c r e p e n c i e s as l a r g e as  five  c e n t i meters. 8.1  R e s u l t s of Harmonic A n a l y s i s A subset of the s e r i e s H02 was generated at h o u r l y  intervals  and c o n s i s t e d of 793 data p o i n t s c e n t e r e d at  hours PST August 2 6 , 1973.  T h i s data was s u b j e c t e d to a  harmonic a n a l y s i s program p r o v i d e d Directorate,  P a c i f i c Region.  Appendix 2 along w i t h t i d a l  zero  by the Marine S c i e n c e s  The r e s u l t s are summarized i n components at Squamish, nine  k i l o m e t e r s north o f the t e s t s i t e , and components at  Point  A t k i n s o n , 35 k i l o m e t e r s south of the t e s t s i t e .  analyses  The  performed on r e f e r e n c e s t a t i o n s were based on a r e c o r d of one y e a r .  Most harmonic components agreed w e l l  and phase except f o r d i u r n a l  length  in amplitude  component KI which was about 16  c e n t i m e t e r s l o w , and s e m i d u i r n a l component S2 which was about five  centimeters high.  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 S 2 , was - 0 . 0 5 6 c e n t i m e t e r s w i t h a 95 per cent c o n f i d e n c e i n t e r v a l ± 0.296 c e n t i m e t e r s .  Fourier  of  t r a n s f o r m r e s u l t s agreed w e l l  51 w i t h the harmonic a n a l y s i s  ( w i t h i n three centimeters f o r  and two c e n t i m e t e r s f o r S 2 ) .  KI  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 d e t e r m i n e d . 8.2  Low Frequency  P o r t i o n of the Power Spectrum  The record l e n g t h f o r s p e c t r a l chosen to r e p r e s e n t a continuous  c a l c u l a t i o n s was  the fundamental data p e r i o d and to  f u n c t i o n at the r e c o r d end p o i n t s .  ensure  Record  length  was 27.969 days and c o n s i s t e d of 65,536 samples. The low frequency presented as a non-averaged Various  tidal  p o r t i o n of the power spectrum i s l i n e spectrum i n f i g u r e 8 . 3 .  s p e c i e s dominated the spectrum at  frequencies  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 The continuum of background energy was a l s o apparent tidal  species, f a l l i n g  frequency.  Low l e v e l  relatively  smoothly w i t h  between  increasing  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 n o i s e l i m i t which c o i n c i d e d with the axis.  hour.  horizontal  The background energy near 0.06 c y c l e s per hour was  somewhat h i g h e r than e x p e c t e d . between d i u r n a l  and s e m i d i u r n a 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 generally  T h i s r e g i o n of the s p e c t r u m ,  disturbances.  The weather was  calm d u r i n g the t e s t p e r i o d except f o r a moderate  south wind which o f t e n appeared at midday and u s u a l l y persisted until  early  evening.  52  108 n  10  cm cy/hr 2  I0~  4  0  0.02  0.04  0.06  0.08  0.16  0.18  0.20  0.22  0.10  0.12  0.14  0.26  0.28  IO i 4  .-4  10  0.14  0.24  F cy/hr  Figure 8.3  Non-Averaged L i n e 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 p r o v i d e d i n  8.4.  figure  T h i s spectrum was p l o t t e d u s i n g l o g a r i t h m i c a v e r a g i n g  i n o r d e r to improve c o n f i d e n c e l i m i t s at high  frequencies.  The most s i m p l e form of l o g - b a n d a v e r a g i n g i s to groups i n powers of two ( 1 , 1 , 2 , 4 , 8 , 1 6 , . . . )  average The scheme  can be extended to i n c l u d e subgroups t h a t c o n s i s t s of powers two as i n ( 1 , 1 , 1 , 1 ) , 4),...  (1, 1, 1, 1 ) ,  (2, 2, 2, 2 ) ,  With t h i s method, the t o t a l number of p o i n t s  i s a c o n v e n i e n t power of two. number of p o i n t s  In g e n e r a l , i f  the  of  (4, 4, 4, averaged  original  is N = 2  and the s i z e of each subgroup  n  is M = 2  m  then the number of p o i n t s 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 w i t h a subgroup  size  of 2 . 3  The complete power spectrum was dominated by d i u r n a l and s e m i d i u r n a l t i d a l  components w i t h h i g h e r s p e c i e s e x t e n d i n g  to n e a r l y one c y c l e per -hour.  Identification  of the two or  three peaks a p p e a r i n g immediately below one c y c l e per hour as tidal  harmonics was not c e r t a i n .  Above one c y c l e per hour the  54 spectral  peaks were l i k e l y s e i c h e s .  The h i g h e s t  resonance peak had a p e r i o d of a p p r o x i m a t e l y The fundamental of l e n g t h  frequency  8.1 m i n u t e s .  p e r i o d 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  (Lv); and depth (h)  is  (Defant 1 958 page 61)  Taking f o r a l e n g t h the d i s t a n c e where the channel  turns,  (L)  basin  between the s i l l  and (h)  and Woodfibre  are  L = 12 km h = 250 m f o r which  T = 8.1 minutes  The second h i g h e s t  frequency  m i n u t e s , was t e n t a t i v e l y fundamental  peak, w i t h a p e r i o d of 1 0 . 8  i d e n t i f i e d i n a s i m i l a r way as the  component between the s i l l  and Squamish,  located  at the head of Howe Sound. D e t a i l e d examination of a few maximums and minimums i n the t i d a l transient  data r e v e a l e d  the o c c a s i o n a l  presence of a  o s c i l l a t i o n with a p e r i o d near 10 m i n u t e s ,  starting  at s l a c k water and l a s t i n g only a few c y c l e s w i t h an amplitude of a p p r o x i m a t e l y  one  The i n c r e a s e  centimeter. i n energy w i t h frequency  per hour was caused i n p a r t by the q u a n t i z a t i o n imposed by l i m i t e d measurement  resolution.  above 10 c y c l e s noise  limit  55  I0"  4  I0'  3  10  10  2  1  I  10  F_  cy/hr  Figure 8.4  F u l l Power Spectrum of S e r i e s H02 F e a t u r i n g Log-Band Averaging  I0  2  56 8.4  Comparison of S t a f f Readings and P r e s s u r e Gauge Readings A b s o l u t e water h e i g h t r e f e r e n c e data was  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 of the t e s t s i t e .  Table  Date  interval  on  II  between Water S u r f a c e L e v e l s and P r e s s u r e Gauge  Sampling S t a f f P e r i o d Hei ght hours  1973  southeast  Amplitude readings were taken over a 20  hour p e r i o d on August 6 , 7, 1973 and over a s h o r t  Difference Readings  provided  Tide State  Mean Di f f e r e n c e c e n t i meters  meters  95%Confi dence limits centimeters  Aug 6  2.0  2.519  high  -2.58  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  -1.57  + 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  .  + 0.31  August 14, September 8 , and September 9 , 1973. the comparisons i s p r o v i d e d  in table II.  A summary of  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 i d not app.ear c o r r e l a t e d tidal  height.  A p r e c i s e s p e c i f i c a t i o n of  absolute  a c c u r a c y was i n d e t e r m i n a t e from the comparisons due to effects  with  but has an upper bound of t h r e e c e n t i m e t e r s .  density Long  term d r i f t  of t i d a l  data measured was l e s s than f o u r  centi-  meters per month, based on August 14 and September 8 , 9 comparisons. is  Time s e r i e s p l o t s f o r the l a s t three  presented in f i g u r e  8.5.  The s i n u s o i d a l  comparisons  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 s u r f a c e waves s i n c e pressure  gauge response was r e l a t i v e l y  the  smooth over the  i ntervals. A review of the August 6 , 7 comparisons indicated a sinusoidal  tendency  i n the data but d i s p e r s i o n  data p o i n t s made t h i s c o n c l u s i o n u n c e r t a i n . oscillations  also  The p e r i o d  of  of  i n f i g u r e 8 . 5 appeared to be i n a range of 50 to  100 m i n u t e s , which was a l s o r e v e a l e d in the power spectrum of figure  8 . 4 with a resonant peak of 7 1 . 9 m i n u t e s .  integration levels)  of the 7 1 . 9 minute resonant peak (above  y i e l d e d a root-mean-square  centimeter.  A numerical  signal  The s u r f a c e waves of f i g u r e  level  background  of 0.28  8 . 5 were  observed  y e t were b a r e l y d e t e c t e d by the bottom-mounted p r e s s u r e This may have been due to s p a t i a l d i f f e r e n c e s  i n amplitude  and p r e s s u r e measurements or to dynamic d e n s i t y changes the water column.  gauge.  in  58  € = STAFF-GAUGE  HORIZONTAL  Figure 8 . 5  +  DATUM  CORRECTION  SCALES: TIME  IN  MINUTES  Time S e r i e s of D i f f e r e n c e s Between Water S u r f a c e L e v e l s and P r e s s u r e 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 to both Oceanographer and Hydrographer. requires  The  shelf is  useful  Oceanographer  boundary c o n d i t i o n s f o r h i s l a r g e - s c a l e t i d a l models  and e s t i m a t e s of the continuum of e n e r g y , d i f f i c u l t to measure in noisy coastal regions, contribute o c e a n i c energy d i s s i p a t i o n . data to p r e d i c t t i d a l and i n d i r e c t l y ,  The  towards c a l c u l a t i o n s of  Hydrographer uses o f f s h o r e  h e i g h t s at c o a s t a l p o r t s both  where t i d a l  directly  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 i n p u t to mathematical models of c o a s t a l In the A r c t i c Ocean, e x t e n s i v e use of s h o r e - b a s e d t i d a l  .  regions.  i c e cover o f t e n p r e c l u d e s the ,  instrumentation.  The bottom-mounted t i d e gauge p r o t o t y p e  described in  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 p a r t per . m i l l i o n at 1000 meters d e p t h .  A single  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 w i t h an a b s o l u t e 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 f o r the gauge  can approach 60 d e c i b e l s a t t i d a l  frequencies.  waves measured w i t h the c o n t i n e n t a l  S p e c t r a of  s h e l f t i d e gauge are  60 subject  to low pass f i l t e r i n g from n a t u r a l  causes such as  depth a t t e n u a t i o n and from sampling t e c h n i q u e s . The V i b r o t r o n  transducer  provides  a frequency  t h a t i s modulated by the p r e s s u r e s i g n a l .  Either  output  frequency  or p e r i o d 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 N y q u i s t f o r the t i d e gauge.  frequency. Careful  The l a t e r f e a t u r e was chosen a t t e n t i o n was p a i d to the  of c a l i b r a t i o n polynomial w i t h the r e s u l t c o m p l i c a t e d polynomial  choice  that a s l i g h t l y  improved accuracy of  more  amplitude  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 r o c e s s i n g elements were  guided  by an aim f o 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 t h redundancy both c o n t r o l  and data s t o r a g e .  in  Recording a ; t i m e - t a g word  w i t h each p r e s s u r e measurement p r o v i d e s  f o r immediate r e c o v e r y  from l o s t data and, i n a d d i t i o n , y i e l d s  statistical  on i n s t r u m e n t o p e r a t i o n .  The mechanical aspect of  information the  i n s t r u m e n t package, though i n e l e g a n t , was f u n c t i o n a l . Field test results  i n d i c a t e d adequate  but were somewhat l i m i t e d w i t h regard to verification  Inequalities  corresponding  specification  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  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 validity.  performance  conversions  restricted  between s u r f a c e wave measurementssand  bottom p r e s s u r e data i n d i c a t e s the  presence of unusual  of  density  possible  time dependence in water column  density  61 structure  of the t e s t  region.  Oceans c o v e r i n g the c o n t i n e n t a l s h e l f do not 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 observed i n the t e s t  would have been u s e f u l f o r e v a l u a t i o n of a b s o l u t e  transducers instrument  One procedure to o b t a i n the l i m i t i s to p l a c e  two or more t r a n s d u c e r s correct  frequencies  region.  As e s t i m a t e of l i m i t i n g s e l f n o i s e of the  performance.  exhibit  in a thermally quiet  the r e s u l t i n g records  environment,  f o 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  transducers  w i t h s p e c t r a l methods, and examine the r e m a i n i n g noncoherent energy which r e p r e s e n t s s e l f - l i m i t i n g n o i s e of the ( I r i s h and Snodgrass  transducers  1972).  The two p r o t o t y p e s  constructed for this project  were  permanently i n s t a l l e d i n the B e a u f o r t Sea of the A r c t i c Ocean in October,  1973.  Recovery of the f i r s t  a n t i c i p a t e d i n A u g u s t , 1974.  data s e r i e s  is  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 Da ta : A n a l y s i s and Measurement Procedures. 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Spectral Analysis of S h o r t I n e r t i a l - I n t e r n a l Wave R e c o r d s . Marine S c i e n c e s D i r e c t o r a t e , M a n u s c r i p t 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 . of Toronto P r e s s , 1972  Toronto:  University  Godin, G a b r i e l . E i g h t Years of O b s e r v a t i o n s on the Water Level a t Quebec and Grandines 1962-1969 P a r t 1 - A n a l y s i s of the T i d a l S i g n a l . Marine S c i e n c e s D i r e c t o r a t e , M a n u s c r i p t Report S e r i e s #31, 1973 Guttman, I r w i n and S . S . W i l k s . Introductory Stati sties. 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 . The Dock & Harbour A u t h o r i t y .  Engineering  " E r r o r s i n Tide Gauges," Vol XLVI11 No 568, Feb 1968  BIBLIOGRAPHY . ( c o n t i n u e d ) H u n k i n s , Kenneth. "Waves on the A r c t i c Ocean," J o u r n a l Geophysical R e s e a r c h . Vol 6 7 , No 6, J u n e , 1962  of  I r i s h , J . D . and F . E . S n o d g r a s s . "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 R e s e a r c h. Vol 1 9 , ( 1 6 5 - 1 6 9 ) , 1972 O p e r a t i o n and Maintenance Manual Model DSP 340 R e c o r d e r , " Kennedy Co. , 1967 Kinsman, B l a i r . Wind Waves. P r e n t i c e - H a l 1 , 1965 L a t h i , B.P.  Englewood C l i f f s , New J e r s e y :  Communication Systems.  New Y o r k : 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 P r e s s u r e Transducer J o u r n a l of Ocean Technology, Vol 2 , No 2 , 1968 Lennon, G.W. Institute 1 966  Technology,  "The I n t e r p r e t a t i o n of Van de C a s t e e l e Diagrams, of C o a s t a l Oceanography and T i d e s . ICOT/IR/8,  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 D e n s i t y V a r i a t i o n s , " I n s t i t u t e C o a s t a l Oceanography and T i d e s . ICOT/IR/7, 1966  of  LeSchack, Leonard A. and R i c h a r d A. H a u b r i c k . "Observations of Waves on an I c e - C o v e r e d Ocean," J o u r n a l of Geophysical R e s e a r c h . Vol 6 9 , No 18, 1964 Munk, W. and D. C a r t w r i g h t . " T i d a l S p e c t r o s c o p y and P r e d i c t i o n , " P h i l . T r a n s . Royal S o c i e t y of L o n d o n , " A 259. (533-581) 1966 Munk, W a l t e r 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 1 7 , 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. Pergamon P r e s s , 1963  Oxford  R o l f e , R.C. " V i b r a t i n g Wire P r e s s u r e Transducer E l e c t r o n i c s , " J o u r n a l of Ocean Technology. Vol 2 , No 2. 1968 S n o d g r a s s , Frank E. "Deep-Sea Instrument C a p s u l e , " S c i e n c e . Vol 1 6 2 , O c t , 1968  BIBLIOGRAPHY U.S.  (continued)  Navy Oceanographic I n s t r u m e n t a t i o n C e n t e r , Vi b r o t r o n P r e s s u r e T r a n s d u c e r , Instrument Fact Sheet #68011, Mar, 1968  Wadhams, P e t e r . " A t t e n u a t i o n of Swell by Sea I c e , " J o u r n a l of G e o p h y s i c a l R e s e a r c h . Vol 7 8 , No 1 8 , J u n e , 1973  APPENDIX 1  Continental  S h e l f Tide Gauge C i r c u i t  Diagrams  66  U J  ^  cc U J  U J Q  cc o£ o ± !  WRITE/STEP SLEW EOR EOF  o o _l o  U J  cc O  < cc  h-  U J  CL  <  r-  T T  -z.  Q  cc  <  MUX CONTROL  _ J  o cc  U J  X - J  U J  <t — I  TIME  o o  CL  t  -R Q —I ID  CD  T T  I I PRESSURE  CC UJ  REFERENCE  h-  START  <  END  >o cc -z. U J  U J  Z>  o UJ cc < CO  o O _l o  X CD  O U_lJ U J  co U J  CO  CO U J  JO  o cc  2:  r-  o o  <  R CRYSTAL OSCILLATOR 447392.43 Hzl  R  R  <f>  AI3 15 18 21  24 25 26 27 28  Tl T2 T3  T4 T5 T6  T7  T8  BI2 T9  TIO Til  TI2  TI3  TI4  CLK  AlON . R j  JAI^>  c AIO>  S8 MASTER RESET GATES  MASTER CONTROL  SAMPLE  SWITCH  INDICATOR  n  ,5.6 K  ,220 PB  PB  SLEW  • SLEW  6.4v  MANUAL SLEW  CONTROL  CONTROL  <f>  EOF >56K  Q  D  C3  C3  Q  4>  =J=O.I  END-OF-FILE  PULSE GENERATOR  «-S8„  MULTIPLEXER AND BUFFER  TPI  TP3  I 1t 1t t  PI  P2 P3 P4  4>  D  0  R  t t t t t M  t—i  P 5 P6 P 7 A3  P8 <£  P9  PIO PI I PI2 PI3  PI4  PI5  4>  A2 R  Al R  -CC  A6  <f>  Q  A8  A5 II  12  c/> 13 14  15  A4 16  17  18  19  2 0 21 V  VIB  OUT SENSITIVITY SELECT  TP4  TP2  FREQUENCY  STATIC  GND  rfn  SAMPLER  TRANSDUCER AND AMPLIFIER  r*-V  B  VOLTAGE REGULATOR  VIBROTRON  0  LOGIC a RECORDER  I2v  CO •GND POWER  SUPPLY  VOLTAGE  REGULATOR  SIGNAL  CONDITIONER  PART NUMBER  CO MPONENT ID ENTIFICATION  DEVICE DESCRIPTION  A  B  7  16,21  CD4001AE  Quad two input NOR  1  CD4002AE  Dual f o u r i n p u t NOR  4  CD4007AE  Dual complimentary p a i r p l u s  2  CD4011AE  Quad two input NAND  1 ,3  CD4013AE  Dual D f l i p  CD4016AE  Quad b i l a t e r a l  CD4017AE  Synchronous decade counter  CD4020AE  B i n a r y r i p p l e counter 14 stage  CD4024AE  B i n a r y r i p p l e counter  CD4049AE  Hex i n v e r t i n g  CD4050AE  Hex n o n - i n v e r t i n g  CA3080  Micropower programmable OTA  CA3082  NPN a r r a y  UA776  Micropower programmable Op Amp  8,11 6  17,19 14,18,20  C  D  2 - 9 15 5,12,13 1 - 4  11,12,13  10 10 2 22 5,6  inverter  flop switch  7 stage  buffer buffer  --> 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 i d a 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  Tidal Component Name  Squamish Ampli tude cm + 0.015  B r i t a n n i a Beach  * Phase  Ampli tude Phase  Pt.  Atkinson  Ampli tude Phase  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  2.7  145.0  2.4  224.7  4.0  144.3  N 0  ]  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  3.0  184.1  4.9  223.5  3.4  202. 3  0.3  190.9  oo  1  e  2  2N N  2  M  2  2  2.9  111.0  1.8  88. 8  2.6  125.7  19.4  136.4  18.3  129.5  19.4  134.7  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  0.2  16.1  0.0  84.3  0.1  301 . 6  0.2  38.4  0.3  342.5  0.1  13.1  M0 M  3  3  73 APPENDIX 2 ( c o n t i n u e d )  Tidal Component Name  Squamish Ampli tude cm + 0.015  Bn* t a n n i a Beach  * Phase  Ampli tude Phase  Pt.  Atkinson  Ampli tude Phase  deg  cm + 0.15  deg  cm + 0.015  deg  0.5  165.2  0.6  178.2  0.7  183. 6  0.1  286.3  0.6  254.0  0.3  227.1  0.4  1 38.9  0.3  1 33.6  0.4  140.9  4  0.9  161 .6  0.9  152.5  0.9  164.3  4 MS  0.2  183.4  0.0  164.0  0.1  147.9  0.4  1 78.6  0.3  1 99.8  0.5  169.9  0.5  37.7  0.6  44.3  0.7  93.5  1 .0  70.2  0.9  72. 7  0.9  66.2  0.8  92. 9  0.9  101 .9  0.7  93.5  0.1  81 . 8  0.0  77.9  0.1  82.4  MK SK  3  MN M  3  4  S N  4  2MN M  6  2MS M  g  8  g  * The e r r o r bound on amplitude r e f e r s o n l y to p r e c i s i o n o r i g i n a l data which was i n u n i t s of f e e t .  of  

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