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Seasonal and secular variations of sea level with special reference to the Canadian Pacific Coast Siebenhuener, Hajo Fritz Wilhelm 1970

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SEASONAL AND SECULAR VARIATIONS OF SEA LEVEL WITH SPECIAL REFERENCE TO THE CANADIAN PACIFIC COAST  by HAJO F.W. SIEBENHUENER Dipl.-Ing., Technische Universitaet B e r l i n , 1969  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF i  MASTER OF APPLIED SCIENCE  in the Department of  C i v i l Engineering  We accept t h i s t h e s i s as conforming  to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA November, 1970  In  presenting  this  thesis  an a d v a n c e d d e g r e e the L i b r a r y I  f u r t h e r agree  for  scholarly  by h i s of  shall  this  written  at make  of  f i n a n c i a l gain shall  Civil  Engineering  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  Date  March 22,  1971  Columbia  I agree  r e f e r e n c e and this  that copying  not  or  for  that  study. thesis  by t h e Head o f my D e p a r t m e n t  is understood  permission.  Department  requirements  for extensive copying of  p u r p o s e s may be g r a n t e d It  the  B r i t i s h Columbia,  it freely available for  that permission  for  fulfilment of  the U n i v e r s i t y of  representatives. thesis  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  - ii-  ABSTRACT In the f i r s t part of this thesis d e f i n i t i o n s of sea l e v e l are given and causes and e f f e c t s of i t s seasonal  and secular v a r i a t i o n s are b r i e f l y  discussed. The second part deals with the numerical determination  of these changes  on the coast of B r i t i s h Columbia. Using raw t i d a l data i n the form of monthly means of sea l e v e l , seasonal  v a r i a t i o n s are determined as annual  o s c i l l a t i o n s with mean amplitudes between 5 and 12 cm for seven stations on the B.C* coast. The  i n v e s t i g a t i o n of secular v a r i a t i o n s i s based on (raw) annual means  of sea l e v e l . These v a r i a t i o n s are e s s e n t i a l l y represented  by linear  trends  which are s t a t i s t i c a l l y s i g n i f i c a n t at the stations VICTORIA, VANCOUVER, POINT ATKINSON and PRINCE RUPERT, where they indicate submergence. Assuming an e u s t a t i c r i s e of sea l e v e l at the rate of 1.0 mm/yr, the influence of land movement on submergence i s estimated. For VICTORIA, a probable land u p l i f t since 1909 and for VANCOUVER, POINT ATKINSON and PRINCE RUPERT a d e f i n i t e land subsidence since about 1943 i s found. The rates of land subsidence range between 1 and 2 mm/yr.  -iii  TABLE OF CONTENTS Page INTRODUCTION  x  1  1. DEFINITIONS OF SEA LEVEL  2  2. FACTORS INFLUENCING SEA LEVEL  3  2.1.  Factors  influencing  Physical Sea Level (PSL)  3  2.1.1. Periodic v a r i a t i o n s  3  2.1.2. Quasi-periodic  6  2.2. Factors  variations  Influencing Physical Mean Sea Level (PMSL)  2.2.1. Movements of the earth's crust  8  2.2.2. Movements o f sea l e v e l 2.3. Factors  10  influencing Derived Mean Sea Level (PMSL)  2.4. Comprehensive consideration  12  of f a c t o r s influencing sea l e v e l  3. SEA LEVEL ON THE CANADIAN PACIFIC COAST 3.1. Presentation  8  and discussion of data  3.2. Analysis of PMSL  15 18 19 22  3.2.1. Seasonal v a r i a t i o n s of DMSL  22  3.2.2. Secular v a r i a t i o n s o f DMSL  24  3.3. Discussion of r e s u l t s  28  CONCLUSION  32  BIBLIOGRAPHY  35  APPENDICES  37  .  - iv -  LIST OF TABLES Page Table I. The long period harmonic t i d a l constituents ( a f t e r Doodson)  4  Table I I , Summary of f a c t o r s influencing DMSL  16  Table I I I . Gauge s t a t i o n index  19  Table IV. Time-spans of available t i d a l records  22  Table V, Amplitude, period and phase l a g of seasonal o s c i l l a t i o n  24  Table VI. Table of regression c o e f f i c i e n t s  28  Table VII. Rates of PMSL, r e l a t i v e and land movement  31  - V-  LIST OF FIGURES Page Figure 1, Components of sea l e v e l v a r i a t i o n at Esbjerg (Denmark)  18  Figure 2, Map of gauge locations on the Canadian P a c i f i c coast  20  -  vl -  LIST OF APPENDICES Page Appendix  1. Sample l i s t i n g  o f d a l l y means o f DMSL f o r ALERT BAY, B.C. (1967)  Appendix 2. Sample l i s t i n g  37^  o f monthly means o f DMSL f o r ALERT BAY, B.C. (1948 - 1968)  Appendix 3. Sample computer o u t p u t o f l e a s t  39  squares f i t o f  monthly means o f DMSL t o t h e f u n c t i o n ZM -  a  D  + a M + A c o s [ziT/TCM - M )] L  Q  f o r ALERT BAY, B.C. Appendix 4. Sample p l o t  43  o f monthly means o f DMSL f o r  ALERT BAY, B.C. and f u n c t i o n  fitted  t o them  45  Appendix 5. L i s t i n g o f annual means o f DMSL Appendix 6. P l o t s  47  o f annual means o f DMSL f o r VICTORIA, B.C.  and FULFORD HARBOUR, B.C. and l i n e a r r e g r e s s i o n Appendix 7. P l o t  Appendix 8. P l o t s  line  57  o f annual means o f DMSL f o r VANCOUVER, B.C.  and POINT ATKINSON, B.C. and l i n e a r r e g r e s s i o n Appendix 9. P l o t  Appendix  linear regression  10, P l o t  11. P l o t and  Appendix  lines  59  o f a n n u a l means o f DMSL f o r TOFINO, B.C. line  61  o f annual means o f DMSL f o r ALERT BAY, B.C.  and l i n e a r r e g r e s s i o n Appendix  55  o f annual means o f DMSL f o r VICTORIA, B.C.  and q u a d r a t i c r e g r e s s i o n  and  lines  line  63  o f annual means o f DMSL f o r PRINCE RUPERT, B.C. linear regression  line  65  12. Sample computer o u t p u t o f l e a s t  squares f i t o f  annual means o f DMSL t o t h e f u n c t i o n Z - a + y  with test  0  3 l  Y  of significance  of  f o r ALERT BAY, B.C.  67  - vii -  ACKNOWLEDGEMENTS Thanks a r e due t o Mr. G. D o h l e r and Mr. S.O. Widen, both o f t h e Canadian H y d r o g r a p h i c S e r v i c e , f o r s u p p t y l n g t h e t i d a l d a t a and a d d i t i o n a l i n f o r m a t i o n used i n t h i s t h e s i s . Furthermore I am g r a t e f u l f o r t h e a d v i c e g i v e n me by Dr. S.H. de J o n g , P r o f . H.R. B e l l and P r o f . S.O. R u s s e l l , a l l o f t h e Department of C i v i l E n g i n e e r i n g o f the U n i v e r s i t y o f B r i t i s h Columbia. In p a r t i c u l a r I w i s h t o thank P r o f . H.R. B e l l f o r c a r e f u l l y c h e c k i n g the m a n u s c r i p t f o r correct  English.  Vancouver November, 1970  H.  Siebenhuener  -  1 .  INTRODUCTION The study of sea l e v e l , the causes and e f f e c t s of i t s changes, and attempts to separate v e r t i c a l movements of the sea from s i m i l a r movements of land i s an aspect of geophysics which has only received world-wide attention i n comparatively recent years. Of even more recent o r i g i n i s the r e a l i z a t i o n by geodesists and hydrographers - to mention only two  kinds  of s p e c i a l i s t s - that each has a common interest in the subject. As r e c e n t l y as f i f t e e n years ago, hydrographers tended to have an exaggerated idea of the accuracy of n a t i o n a l l e v e l l i n g nets, while geodesists tended to have s i m i l a r misconceptions  of the s t a b i l i t y of sea l e v e l .  It i s one thing to record f a c t s but quite another to interpret them, and the study of sea l e v e l i s no exception to t h i s general p r o p o s i t i o n . We wish not only to observe and record what has happened and what i s happening, but also to account f o r what i s observed,  i n order, i f p o s s i b l e , to look  ahead and forecast l i k e l y trends. Once one s t a r t s to look for causes of changes i n sea l e v e l , the f i e l d widens appreciably. We find that i s necessary to have at least a cursory knowledge of the growth arid decline of g l a c i e r s , of c l i m a t i c changes, of c r u s t a l movements of the earth and many other f a c t o r s . In fact the study of sea l e v e l i n t e r l o c k s with many other - perhaps nearly a l l - geophysical problems* In view of the above, t h i s study i s subdivided into three main sections. In preparing the t h e s i s the necessity for and the lack of clear-cut d e f i n i t i o n s became obvious; they are given i n section 1. In section 2 some of the underl y i n g concepts are summarized. The  intention i s to convey some idea of the  complexity and v a r i e t y of f a c t o r s influencing sea l e v e l . In section 3 the r e s u l t s of the numerical work are given. This section c o n s i s t s e s s e n t i a l l y  - 2 of a s t a t i s t i c a l analysis of a v a i l a b l e t i d a l data on the coast of B r i t i s h Columbia and an i n t e r p r e t a t i o n of the r e s u l t s . No attempt i s made to correct raw  t i d a l data for d i s t u r b i n g meteorological  influences such as a i r pressure,  temperature and p r e v a i l i n g winds.  1. DEFINITIONS OF  The  SEA LEVEL  i n v e s t i g a t i o n in the following sections makes frequent  use of  three  terms which are defined as follows:  i ) "Physical Sea L e v e l " (PSL)  at any place i s the physical boundary  between ocean and a i r . i i ) "Physical Mean Sea L e v e l " (PMSL) at any place i s the average of the continuously  changing height of Physical Sea Level with respect  land over a l l stages and periods of a l l astronomical  to  tides.  i i i ) "Derived Mean Sea Level" (DMSL) at any place i s the average of measured values of Physical Sea Level over a c e r t a i n period and  i s referenced  to a bench mark and hence a datum. The common feature of the three kinds of sea l e v e l as defined above i s t h e i r time and  space dependence; the l a t t e r i s not dealt with in t h i s thesis  since i t can only be studied on a world-wide basis. D e f i n i t i o n i ) i s self-explanatory. PSL  and PMSL d i f f e r in that PSL  i s affected by the t i d e s whereas PMSL  i s not affected by the t i d e s . The difference between PMSL and DMSL i s a conceptual one and r e s t s on f a c t that PMSL e x i s t s regardless of the existence of man DMSL comes into being only when man  the  and h i s action while  builds a t i d e gauge s t a t i o n , more or less  continuously measures sea l e v e l s and analyzes them.  - 3 Two  examples i l l u s t r a t e the concept behind t h i s d i s t i n c t i o n :  1) It makes complete sense to say: "The station No.  173  i s 9.37  annual value of DMSL in 1948  for  feet above datum." Replacing DMSL by PMSL y i e l d s  nonsense because PMSL cannot be measured and hence cannot be represented by a number. 2) While i t i s in order to say: "PMSL i s subject to secular v a r i a t i o n s due to g l a c i a l a c t i o n " , replacement of PMSL by DMSL does not make sense because a DMSL value as such i s not affected by physical action. PMSL i s best thought of as a geophysical phenomenon whereas DMSL i s best regarded as a number which describes t h i s phenomenon more or less accurately. This d i s t i n c t i o n proves to be useful in the discussion of various f a c t o r s influencing sea  the  level.  2. FACTORS INFLUENCING SEA LEVEL Because of the limited scope of t h i s study the discussion of f a c t o r s influencing sea l e v e l must be r e s t r i c t e d to a b r i e f description of  the  e f f e c t of each f a c t o r . Where a v a i l a b l e , a numerical estimate of the e f f e c t on sea l e v e l i s given. In order to f a c i l i t a t e reference  to f a c t o r s , each of  them i s numbered in round brackets. 2.1.  Factors  influencing Physical Sea Level  (PSL)  The physical boundary between ocean and a i r varies with time; the v a r i a t i o n s may  be broken down into s t r i c t l y periodic and quasi-periodic or seasonal  components (Rossiter, 1962).  2.1.1. Periodic v a r i a t i o n s (1) The and  Tides. The  t i d e s are caused by the variable a t t r a c t i o n of the moon  the sun and consist of many harmonic constituents, the periods of  - 4 -  which range from several hours up to approximately nineteen  years.  D a i l y , monthly and yearly values of DMSL are normally derived from observed data by methods s p e c i f i c a l l y designed to eliminate, as e f f i c i e n t l y as p o s s i b l e , t i d a l o s c i l l a t i o n s having periods up to and  including a  lunar day. A d a i l y mean, f o r example, i s generally computed from at i n t e r v a l s of an hour by simple averaging,  observations  by a p p l i c a t i o n of numerical  f i l t e r s , or by integration of graphical records. The f i g u r e s so  obtained,  when averaged over a month or a year, s t i l l contain small contributions from some long period constituents. These long period constituents and some properties of them are l i s t e d i n Table I, taken from Doodson's harmonic development of the t i d e generating  p o t e n t i a l (Doodson, 1921).  They are relevant when one considers seasonal and secular v a r i a t i o n s .  Table I. The long period harmonic t i d a l constituents ( a f t e r Doodson)  Name Lunar f o r t n i g h t l y Luni-solar fortnightly Lunar monthly Solar semi-annual Solar annual Nodal  Symbol Mf Msf Mm Ssa Sa  -  Angular speed in degrees per mean solar hour 1.0980 1.0159 0.5444 0.0821 0.0411 - 0.0022  Period in days  Equilibrium^ amplitude in cm 2.10 0.18 1.11 0.98 0.15 - 0.88  13.7 14.8 27.6 182.6 365.2 18.62yrs  The amplitudes are associated with the l a t i t u d e c o e f f i c i e n t (1 - 3cos S ) , where Q i s c o - l a t i t u d e .  The amplitudes are those appropriate to the equilibrium t i d e , the t i d e that would be experienced i n an ocean which completely covers the earth and responds instantaneously to the t i d e generating  forces of  the sun and the moon. In nature the presence of i r r e g u l a r c o a s t l i n e s and v a r i a t i o n s i n bottom topography prevent the equilibrium t i d e s from  being r e a l i z e d i n amplitude and phase, unless t h e i r period i s so long that equilibrium may be assumed to e x i s t . The lunar f o r t n i g h t l y and monthly t i d e s Mf and Mm are generally very small i n size and have not evoked much i n t e r e s t . The small l u n i - s o l a r t i d e Msf, however, has the same period as a larger o s c i l l a t i o n generated by t i d a l v a r i a t i o n s i n shallow depths; thus i n coastal areas and estuaries Msf i s generally quite unrelated i n amplitude and phase to i t s equilibrium form. Monthly values of DMSL w i l l obviously contain n e g l i g i b l y small contributions from Mf, Msf and Mm. Their most s t r i k i n g feature i s the seasonal v a r i a t i o n , which i s customarily represented  by the s o l a r annual and  semi-annual t i d e s , Sa and Ssa, though i n fact by f a r the greater part of these o s c i l l a t i o n s i s not of t i d a l o r i g i n but of meteorological or oceanographic o r i g i n (See f a c t o r s (2),(3) below). The l a t e s t attempt to estimate the t i d a l contributions to seasonal v a r i a t i o n s was undertaken by L.F. Ku, who applied power spectra analysis to monthly means of DMSL (Ku, 1970). H i s values of Sa f o r the North A t l a n t i c and North P a c i f i c coast are i d e n t i c a l and are about 1.2 cm. The nodal t i d e a r i s e s from the precession of the moon's nodes with a period of 18.62 years. I t i s the slowest o s c i l l a t i o n of those given by Doodson. There are sound dynamic reasons f o r b e l i e v i n g that i n nature t h i s t i d e should have an equilibrium form, s u i t a b l y corrected f o r the presence of larger land masses, but confirmation from observations i s d i f f i c u l t to obtain. Comparatively  few long r e l i a b l e s e r i e s of DMSL  e x i s t f o r study and i n l a t i t u d e 50° the amplitude to be sought should only be of the order of 10 mm, whereas the standard deviation of 19 annual values of DMSL may vary between 20 and 80 mm depending on the magnitude of random v a r i a t i o n s from various sources which are always present. R o s s i t e r writes: "The t h e o r e t i c a l existence of t h i s t i d e i s frequently  - 6 used as an argument f o r taking 19-yearly means, or taking a 19-year span of observations when examining data for v a r i a t i o n s of many kinds, yet i t s d i s t r i b u t i o n and magnitude cannot be said to have been determined a n a l y t i c a l l y " ( R o s s i t e r , 1962). The s i t u a t i o n i s s i m i l a r , and for much the same reasons, i n the case of the pole t i d e . This o s c i l l a t i o n which has a period of approximately 14 months was not included i n Doodson's l i s t of t i d a l constituents, but may be expected to exist as a r e s u l t of the i n s t a b i l i t y of the earth's instantaneous  axis of r o t a t i o n . I t has been shown that the  equilibrium form of t h i s t i d e should have an amplitude of the order o f 5 mm (Haubrich and Munk, 1959). Attempts to i d e n t i f y i t i n DMSL data appear to have confirmed  the existence of an o s c i l l a t i o n with a period  of 14 months, though i n general the amplitudes are more than twice the expected value. In contrast to these s t r i c t l y periodic v a r i a t i o n s which are due to g r a v i t a t i o n a l forces and the periods of which can be derived a n a l y t i c a l l y from the equilibrium theory of t i d e s , quasi-periodic v a r i a t i o n s are due to f a c t o r s r e s t r i c t e d to the earth or parts of i t . 2.1.2. Quasi-periodic v a r i a t i o n s Quasi-periodic changes i n PSL are those of seasonal nature. Monthly means of DMSL at any s t a t i o n show a more or less consistent pattern year by year, and these have been i n t e n s i v e l y studied on both a l o c a l and a global scale ( L i s i t z i n and P a t t u l l o , 1961; P a t t u l l o , 1963). There are at least three f a c t o r s involved which may be c l a s s i f i e d as "meteorological", "oceanographic" and "fresh water flow". (2) Meteorological e f f e c t s . Meteorological e f f e c t s account f o r a considerable  - 7 -  part of the seasonal v a r i a t i o n in l a t i t u d e s above 45°. They are the response of PSL to seasonal changes in atmospheric  pressure and pre-  v a l l i n g winds. I f the time rate of change i s slow, as discussed here, PSL acts almost instantaneously as an inverted water barometer; t h e o r e t i c a l l y i t should r i s e 1 cm per 1 mb f a l l  in a i r pressure and  v i c e versa. In a l l l a t i t u d e s seasonal movements and v a r i a t i o n s i n i n t e n s i t y of high and low pressure systems r e s u l t in sea l e v e l changes which may  amount to 8 cm in amplitude.  Wind f i e l d s may  be defined in terms of a i r pressure d i s t r i b u t i o n s  which vary with the seasons. Hence the tangential stress exerted by the wind on the surface layers of the sea also has a seasonal component. This stress produces wind-driven currents which always r e s u l t in gradients in the water surface. Such gradients are most marked along the shores of shallow and p a r t i a l l y enclosed seas. (3)  Oceanographic e f f e c t s . These e f f e c t s , combined with meteorological components, account Regardless of how  f o r seasonal v a r i a t i o n s of PSL in lower  latitudes.  they are generated, great ocean currents such as the  Gulf Stream create surface gradients with seasonal v a r i a t i o n s . Of more d i r e c t oceanographic  o r i g i n are s t e r i c changes in PSL. A s t e r i c  phenomenon i s one which involves the molecular dimensions of the material in question. In sea water, s t e r i c e f f e c t s are brought about by temperature changes and by variations in s a l i n i t y (and thus d e n s i t y ) . Observations of the time-dependent structure of density with depth in the oceans have been used to compute seasonal changes in s t e r i c i t has been shown that over large areas these v a r i a t i o n s can for  level;  account  a large proportion of observed changes in PSL. For instance, a  seasonal r i s e and f a l l of shelf and estuary water temperatures O  may  exceed something of the order of 10 C over a 10 m depth range; the  - 8 -  calculated e f f e c t would be 15.5 mm  s t e r i c r i s e and  fall.  (4) Fresh water flow. Fresh water flow i s the t h i r d major cause f o r quasip e r i o d i c changes i n PSL. Whether due to monsoon r a i n s or melting snow, the flow i s e s s e n t i a l l y seasonal, almost to the extent of being p r e d i c t a b l e . In the v i c i n i t y of a r i v e r mouth t h i s effect may  amount to 10  In concluding t h i s section on f a c t o r s influencing PSL  i t may  cm.  be mentioned  that the usual amplitude of "annual t i d e s " , as seasonal v a r i a t i o n s are sometimes c a l l e d , i s 10 to 15 cm ( P a t t u l l o , 1963).  2.2. Factors influencing P h y s i c a l Mean Sea Level (PMSL)  According to the d e f i n i t i o n of PMSL, one may  imagine PMSL as a PSL which  i s free of the e f f e c t of the astronomical t i d e s . Since i t i s possible to free PSL of astronomical t i d e s only i f a span of about 19 years i s considered, obviously the influence of "annual t i d e s " i s also eliminated. However, the e l i m i n a t i o n of astronomical and annual t i d e s does not s t a b i l i z e PMSL. Since slow but continuing changes in PMSL are a common feature at most s t a t i o n s , i t i s customary to r e f e r to them as secular changes, and to consider them in terms of steady changes i n annual DMSL. For s i m p l i c i t y and since t h e i r d e f i n i t i o n from observed data i s not u s u a l l y p r e c i s e , a l i n e a r change i s assumed, although there i s no p h y s i c a l reason to j u s t i f y a l i n e a r law. In f a c t , i t has been considered in some instances that quadratic or even cubic mathematical expressions describe secular v a r i a t i o n s more p r e c i s e l y . Since PMSL i s considered with respect to land, the f a c t o r s influencing i t can be subdivided into v e r t i c a l movements of the earth's crust and movements of sea l e v e l ( V a l e n t i n , 1952).  2.2.1. Movements of the earth's crust (5) Tectonic movements. Deformations of the crust of the earth i n g e o l o g i c a l  - 9 eras are referred to as tectonic movements. They are caused by i s o s t a t i c adjustment, orogenesis (mountain building) and/or sedimentation. (5a) Tectonic movements due to i s o s t a t i c adjustment. These movements are encountered  i n formerly glaciated regions. During an ice age,part of  the aqueous portion of the earth i s bound to the continents in the form of extensive inland icecaps. As a consequence, continents are r e g i o n a l l y loaded while the pressure of water masses on the ocean f l o o r s decreases everywhere. In order to restore equilibrium, loaded continental regions must sink and a l l ocean f l o o r s i n the world must r i s e . When icecaps melt during a "warm" period, the opposite process takes place and PMSL r i s e s again. Continental regions are then r e l i e v e d and tend to r i s e to t h e i r o r i g i n a l l e v e l again, while the ocean f l o o r s are depressed by the increased water load. Today, maximum rates of i s o s t a t i c u p l i f t of land of nearly 40 mm/yr a f t e r deglaciation have been measured i n southeast Alaska (Hicks and Shofnos, 1965). (5b) Tectonic movements due to orogenesis. The forming of mountains, believed to be caused mainly by tangential compression  of the earth's c r u s t ,  takes place i n so-called orogenic b e l t s which are regions having zones of strongly negative g r a v i t y anomalies (subsidence) and strongly p o s i t i v e g r a v i t y anomalies ( u p l i f t ) . The l a t t e r today generally correspond to the folded mountainous b e l t s . This phenomenon i s i n d i c a t i v e of an incomplete  i s o s t a t i c compensation. The rates of u p l i f t or subsidence  vary considerably according to the i n t e n s i t y of seismic a c t i v i t y i n the region considered. (5c) Tectonic movements due to sedimentation. Sedimentary basins are, geol o g i c a l l y speaking, c l a s s i f i e d as "contemporary geosynclines" of various c l a s s e s . As a r u l e , they are i d e n t i f i e d geomorphologically by t h e i r long,, low, sandy coasts. Although t h e i r o u t l i n e s are straight and the  - 10 -  hinterland may d i s p l a y wide areas of recently emerged c o a s t a l p l a i n s , these coasts are often coasts of submergence''. From deep bores, i t i s apparent that these basins have been discontinuously in subsidence for 6  periods of the order of 10  9  to 10  years. However, the rates of  subsidence  are very slow, being less than 0.1 mm/yr. (6) Atectonic movements. Beside these more or less extensive movements, r e g i o n a l l y limited processes a f f e c t PMSL. Sag due either to sedimentary compaction or to sedimentary collapse causes l o c a l subsidence of the coast and leads to an apparent r i s e of PMSL. To i l l u s t r a t e , great man-made works, c o a s t a l engineering works, harbours and harbour j e t t i e s i n the v i c i n i t y of a gauge s t a t i o n can simulate trends in PMSL, the rate of which i s hard to assess. 2.2.2. Movements of sea l e v e l In addition to the movements of the earth's crust or parts of i t discussed above, world-wide and simultaneous  changes of the oceans influence PMSL.  They are r e f e r r e d to as e u s t a t i c changes and are mainly due to g l a c i a l action. (7)  Glacio-eustasy. Glacio-eustasy i s caused by the world-wide e f f e c t of a hydrological imbalance between world moisture transport to the continents (snow) and, in reverse, to the oceans (meltwater). The processes i n g l a c i a l periods of the earth's h i s t o r y has  imbalance of these especially  affected the volume of ocean water and the p o s i t i o n of PMSL. In each ice age, part of the hydrosphere was bound to extensive inland icecaps thus making sea l e v e l f a l l on a world-wide basis; during each warmer period the ice melted and PMSL rose again.  1) The term "submergence" implies that part of the land area has become inundated by the sea but does not imply whether the sea rose over the land or the land sank beneath the sea.  In  attempting to estimate the magnitude of the changes involved, two  methods may be employed: f i r s t , one may measure the area of g l a c i a t i o n and m u l t i p l y i t by the mean thickness of i c e , thus obtaining the volume of  i c e . A knowledge of the volume of ocean water may then be used to  estimate the change in PMSL; second, one may t r y to locate the geomorphol o g i c a l and geological marks of o l d shorelines by f i e l d  inspection,  d r i l l i n g s and soundings, and supplement the information gained by radiocarbon dating. Using the f i r s t method and allowing f o r i s o s t a t i c u p l i f t of  the r e l i e v e d ocean f l o o r s , Fairbridge estimates that during the last  ice age PMSL was about 100 m below present PMSL. A complete melting of a l l e x i s t i n g g l a c i e r s would r e s u l t i n an eustatic r i s e of PMSL of about 35 m ( F a i r b r i d g e , 1961b). Applying the second method, Mathews ascertained that at the shore of southwestern  B r i t i s h Columbia an eustatic r i s e of PMSL at a mean rate of  1.2 mm/yr has taken place f o r the l a s t 8000 years (Mathews et a l . ,  1970).  This figure agrees with the r e s u l t s of a pioneer study by Gutenberg using data from world wide t i d e gauge records and suggesting an eustatic r i s e of PMSL at 1.1 mm/yr during the f i r s t h a l f of t h i s century (Gutenberg, 1941). A more recent paper (Munk and Revelle, 1952) suggests a figure of 1.0 mm/yr which w i l l be referred to i n section 3. (8) Other eustatic changes. Apart from glacio-eustasy, two other s i g n i f i c a n t factors i n world-wide change of PMSL are recognized;  sedimento-eustasy,  due to accumulation of sediments i n ocean basins, thus causing a one-way, p o s i t i v e s h i f t ; and tectono-eustasy, due to modification i n the shape of ocean basins because of tectonic action, thus being either p o s i t i v e or negative i n e f f e c t . Both of these changes are related to the dimensions of  the container while glacio-eustasy r e l a t e s to the volume of the  contents. I t has been estimated that the sedimento-eustatic r i s e ln PMSL  - 12 amounts to 0.01 to 0.02 mm/yr. Even i f the e f f e c t s of tectono-eustasy and sedimento-eustasy should happen to be of the same sign during a c e r t a i n stage of the earth's h i s t o r y , the rate of change could not be expected to be greater than 0.03 mm/yr. Thus they are not appreciable in terms of human h i s t o r y . Summarizing, i t can be said that tectonic and e u s t a t i c movements are the main components influencing PMSL. I t i s obvious that they also a f f e c t PSL.  2.3.  Factors influencing Derived Mean Sea Level (DMSL)  Changes i n PMSL can only be considered t h e o r e t i c a l l y and q u a l i t a t i v e l y ; quantitative statements about the rates of change are only possible v i a DMSL. One has to e s t a b l i s h a t i d e gauge s t a t i o n , appropriately equipped with measuring devices, reference i t to a bench mark, and record values of PSL over a long period. The values of DMSL thus obtained may or may not represent the p o s i t i o n of PMSL. This discrepancy i s due to the fact that DMSL i s affected by various f a c t o r s which have nothing to do with PMSL but r e l a t e only to the gauge and i t s handling. In general these f a c t o r s have the character of e r r o r s , and the more e f f e c t i v e l y they are eliminated, the more c l o s e l y w i l l DMSL coincide with PMSL. (9) Errors of reading the l e v e l on the t i d e pole. To check automatic t i d e gauges i t i s necessary  to read sea l e v e l on the corresponding  pole ( s i t u a t e d i n the immediate v i c i n i t y ) at least once a day.  tide Since  these readings are used to correct measurements obtained from automatic gauges, t h e i r reading errors influence those measurements. Random reading errors a r i s e from sea waves, the q u a l i t y of the markers, the length of the l i n e of sight to the pole, l i g h t i n g conditions ( p o s i t i o n of the sun), and the p e c u l a r i t i e s of the observer. If measurements are taken once a day, the r e s u l t i n g standard deviation i n an annual value of DMSL  - 13 -  Is approximately + 1 mm. The systematic  errors r e s u l t i n g from errors  in the scale of the pole and from errors r e s u l t i n g from connecting i n d i v i d u a l 1 meter (or foot) sections of the pole are of the same order of magnitude (+ 1 mm). (10)  Errors i n the behaviour of the t i d e gauge. Instrumental errors of a tide gauge can r e s u l t i n changes i n the recording  scale, i n the rate  of feed of the recording tape, i n the distance between the time markers, and  i n the height or additive constant of the t i d e gauge. Small changes  in the recording  scale do not influence the accuracy of determination  of DMSL, since maximum and minimum values are affected a l i k e . Changes in the recording tape feed can r e s u l t i n an error i f printed tape i s used, although t h i s error i s n e g l i g i b l e . Changes in height of the t i d e gauge or i n the additive constant have a d i r e c t bearing on DMSL. However, they are eliminated by comparing the recordings with the t i d e pole (11)  observations.  Errors made in analysing  the ntareograms. Variations i n the dimensions  of the printed recording tapes p r i o r to measurement and errors i n the d i v i s i o n s give r i s e to differences i n the scale of the t i d e gauge and that of the printed subdivisions. The errors i n length of the paper, i f properly stored, are less than 1 : 1000. This a d d i t i o n a l small error in scale has no bearing on the c a l c u l a t i o n of DMSL. The standard deviation when evaluating the mareograms can be as large as + 5 mm f o r a s i n g l e value on a scale up to 1 : 20. The r e s u l t i n g standard deviation f o r an annual DMSL value amounts to about + 0.2 mm i f four measurements are taken each day. (12) L e v e l l i n g e r r o r s . In order to f i x and to check the height of the zero point of the scale on the t i d e pole with reference to the t i d e gauge datum ( t i d a l or chart datum), the height differences r e l a t i v e to the  -  t i d e gauge bench marks s i t u a t e d  14 -  i n t h e v i c i n i t y a r e n o r m a l l y measured  a n n u a l l y . I n t h i s p r o c e s s , v a r i o u s random and s y s t e m a t i c e r r o r s o c c u r and  their  i n f l u e n c e on t h e DMSL o f any g i v e n year  n a t u r e . Today, a mean e r r o r i n double  i s o f a systematic  l e v e l l i n g o f + 0.5 t o 1.0 mm/"\/km'  can be o b t a i n e d w i t h c a r e f u l o b s e r v a t i o n , depending on t h e type o f instrument  employed and t h e d i s t a n c e t o be c o v e r e d . R e l a t i v e l y l a r g e  a d d i t i o n a l e r r o r s a r e i n t r o d u c e d as a r e s u l t o f measuring t h e c o n n e c t i o n between t h e s c a l e o f t h e gauge and t h e t i d e p o l e because t h e l a t t e r f r e q u e n t l y i s n o t e a s i l y a c c e s i b l e f o r l e v e l l i n g . I n a d d i t i o n , random h e i g h t e r r o r s o f t h e t i d e gauge bench marks e x e r t t h e same i n f l u e n c e . Thus t h e s t a n d a r d d e v i a t i o n i n an annual l e v e l l i n g e r r o r s c a n be expected (13)  v a l u e o f DMSL r e s u l t i n g  from  t o be about + 2 mm.  E r r o r s i n h e i g h t . The main c o n d i t i o n t o be met by a t i d e p o l e i s t h a t i t s h e i g h t must remain c o n s t a n t o r t h a t p o s s i b l e e r r o r s i n h e i g h t must be taken  i n t o c o n s i d e r a t i o n . I f a change i n h e i g h t due t o a t e c t o n i c  movements ( f a c t o r ( 6 ) ) i s d e t e c t e d w i t h t h e a i d o f annual checks,  levelling  i t i s n o t p o s s i b l e t o s t a t e a n y t h i n g d e f i n i t e about t h e temporal  c o u r s e o f t h e change. The s t a n d a r d d e v i a t i o n a s s o c i a t e d w i t h c o n d i t i o n f o r an annual  v a l u e o f DMSL i s e s t i m a t e d  this  t o about + 1 mm t o  + 2 mm. The h e i g h t s o f bench marks, sometimes a t t a c h e d t o b u i l d i n g s , a r e n o t always c o n s t a n t  either.  To sum up, t h e f o l l o w i n g e r r o r components n o r m a l l y have a b e a r i n g on an annual  v a l u e o f DMSL:  - E r r o r s o f r e a d i n g t h e l e v e l on t h e t i d e pole  •  e^ «• + 1.0 mm  - Errors i n the t i d e pole scale and  installation  - E r r o r s made i n a n a l y s i n g t h e mareograms  &2 " — e  01111  - + 0.2 mm  - 15 -  - L e v e l l i n g errors and errors in measuring connection of bench mark to t i d e pole  •  - Variations i n the height of the t i d e pole  e  4 " i 2.0 mm ,  e^ «•+ 1.5 mm  A comparison of i n d i v i d u a l error components shows that the main sources of errors a r i s e from height checks and height changes of the t i d e pole. When they are considered over decades, the errors quoted are random and the corresponding t o t a l standard deviation associated with annual values of DMSL can be computed from the law of error propagation: ~\ l~2  Total standard deviation ™ \ / i e  This figure of + 3ram(0.01  +  e  2  +  2  e  3  +  e  2 4  +  e  5  2  2 « + 3 mm (0.01 f t ) . -1  f t ) i s also given by Montag (Montag, 1970)  while Rossiter states a more o p t i m i s t i c but rather u n r e a l i s t i c estimate of + 1 mm ( R o s s i t e r , 1962).  2.4.  Comprehensive consideration of f a c t o r s influencing sea l e v e l  Once one t r i e s to determine changes i n sea l e v e l numerically  one has  to deal with DMSL values. Now DMSL i s influenced not only by the f a c t o r s mentioned i n section 2.3.,  but obviously also by f a c t o r s (1) to ( 8 ) ,  i n c l u s i v e , these f a c t o r s being of widely d i f f e r e n t o r i g i n . Table II gives a summary of the f a c t o r s which tend to produce seasonal and secular changes 2 of DMSL . The observations are only the ultimate resultant of a l l components. In h i s paper "An Analysis of Annual Sea Level Variations i n European Waters" Rossiter t r i e d to separate some components using annual values of DMSL, meteorological was  and astronomical data (Rossiter, 1967). The investigation  based on a mathematical model of the form  2) There are other factors which a f f e c t the basic height ( i . e . an a r b i t r a r y working datum) and/or cause stochastic contributions to values of DMSL. The reader interested i n those factors i s referred,to the references (Wemelsfelder, 1970) and/or (Montag, 1970).  Table I I . Summary of factors influencing DMSL  Movements of the earth's crust Tectonic Factor No. Cause  Effect  (5)  Movements of sea l e v e l  Atectonic  Eustatic  (6)  (7),(8)  Localized subsidence of land  World-wide r i s e of DMSL  7  Character  Aneustatic (1),(2),(3),(4)  Glacio-eustasy, T i d a l movements, Isostatic adjustm. orogenesis Various kinds sedimento- and meteorological tectonoof sag sedimentation * oceanographic eustasy effects,freshwater U p l i f t and/or subsidence o f continents and ocean f loors Secular  Detectable by  Precise l e v e l l i n g plus t i d e gauge records  Appr. rate of change  Max. rate of change 40 mm/yr (Alaska)  Unpredictable Precise levelling  Varies considerably  As to time and l o c a l l y limited r i s e and f a l l of DMSL  Secular  Periodic  Tide gauge recordsv  Tide gauge records  Rise at about 1.0 mm/yr  Movements assoc. with the gauge  Varies according to period  (9),(10),(ll),(12),(13)  Operation of t i d e gauge  Height changes of t i d e pole  Errors i n observation Careful operation of gauge  + 3 mm/yr (+ 0.01 f t / y r ) (Accuracy of annual DMSL value)  I  t—»  - 17 -  Z where  y  -  Y  P  +  5Z r r b  B  +  c  i  c o s  < ) • c s i n ( N ) • <(> , N  2  Y  Is an annual value of DMSL, referred to some a r b i t r a r y working datum, f o r the year Y, Y i s the year number r e l a t i v e to 1900, an annual mean value of a i r pressure, corrected to "mean sea l e v e l " , at s t a t i o n r , f o r the year Y, N i s the mean longitude of the moon's ascending node, and <£y contains the contributions to Z  y  from a l l other sources.  The c o e f f i c i e n t s a , b , c, and c_ are to be determined by regression P r I 2 computations according to the method of least squares. Thus i n the above equation the polynomial  ^ ]  a  Y p  P  represents a secular v a r i a t i o n , providing  the choice between a l i n e a r (p-1), a quadratic (p~2) and a cubic (p-3) expression. The term  ^ jb B r  accounts for atmospheric  contributions and  r =i  the terms CjCos(N) and c^sinCN) express the o s c i l l a t i o n due to the nodal 3 t i d e . A graphical representation of the various components of Zy i s given i n Figure 1 for Esbjerg, Denmark (Courtesy of Royal Astronomical  Society,  London). For purposes of t h i s study, the most important c o n t r i b u t i o n to the observations i s the secular v a r i a t i o n . I t i s the resultant of a r e l a t i v e movement between sea l e v e l and land and i s produced either by s h i f t of the land ( u p l i f t or subsidence)  or by eustatic changes i n PMSL, or both. A  p o s i t i v e secular v a r i a t i o n (as shown i n Figure 1) i s referred to as coastal submergence while a negative v a r i a t i o n i s referred to as emergence. The introduction of these new terms leads to the second part of t h i s t h e s i s . Considering only the coast of B r i t i s h Columbia, seasonal v e r i a t i o n s in DMSL and trends of emergence and/or submergence are investigated. 3) Further explanation of the terms i s found  i n ( R o s s i t e r , 1967)  -  Figure  1. Components o f sea l e v e l v a r i a t i o n  at Esbjerg,  18 -  Denmark  ( U n i t s a r e mm)  Esbjerg  o IO  et  T  200  I  I  Observotlons  100  200 Secular  variation  100  100 r-  Atmospheric  contributions  -100'-  - 5 0 >-  Nodal  tide  Residuals  (Courtesy  o f Royal A s t r o n o m i c a l  S o c i e t y , London)  3. SEA LEVEL ON THE CANADIAN PACIFIC COAST  As  i n d i c a t e d i n the i n t r o d u c t i o n , t h i s s e c t i o n i s concerned w i t h the  numerical on The  determination  o f seasonal  and s e c u l a r v a r i a t i o n s In sea l e v e l  t h e c o a s t o f B r i t i s h Columbia, based on monthly and annual DMSL v a l u e s . p r e s e n t a t i o n and d i s c u s s i o n o f the data  i s followed  by t h e i r a n a l y s i s .  - 19 3.1. Presentation and discussion of data  The "Water Survey of Canada" and the "Canadian Hydrographic Service" operate a series of permanent gauging stations along the Canadian P a c i f i c coast. Their locations are shown i n Figure 2. Seven of these stations have s u f f i c i e n t l y long records f o r purposes o f t h i s study. The seven stations are l i s t e d in Table III together with geographic  p o s i t i o n , bench mark  and datum information of each. Table I I I . Gauge station index Sta.No. 168 169 170 171 172 173 175  Location Victoria Fulford Harbour Vancouver Point Atkinson Tofino A l e r t Bay Prince Rupert  Latitude North 48°25.47' 48 45.84' 49 17.35' 49 20.26' 49 09.30' 50 35.23' 54 18.90'  Longitude West 123"22.17' 123 26.90' 123 06.98' 123 15.15' 125 54.50' 126 56.78' 130 19.70'  Bench mark El.(ft) No. ,15.40 737-J 12.16 HS-1-1952 Brass Plug 42.15 HS-118-1950 21.33 12.93 HS -1-1940 HS-1947 24.59 32.49 HS-1944  Reference datum Chart Datum Chart Datum Chart Datum Chart Datum Chart Datum Chart Datum Chart Datum  At V i c t o r i a and Vancouver the primary bench marks as stated i n the above table are also used f o r geodetic purposes while at the other stations bench marks were e x c l u s i v e l y established f o r hylrographic purposes (HS « Hydrographic 4 Service). Elevations of the bench marks are those above Chart Datum . The t i d a l data were made a v a i l a b l e by the Canadian Hydrographic Service in form of d a i l y values of DMSL. They are given i n feet and decimals of a foot and stored on punched cards which are accompanied by a printed computer output. A sample page of t h i s l i s t i n g i s shown i n Appendix 1. I t shows the d a i l y values of DMSL observed at the gauge station of ALERT BAY i n 1967. The following a d d i t i o n a l information was a v a i l a b l e f o r each of the seven stations: - a description of the gauge station together with a chart showing the location 4) Chart Datum i s a low water datum which by international agreement i s so low that the t i d e seldom f a l l s below i t . It i s used only i n the v i c i n i t y of the gauge location and d i f f e r s from place to place, depending on the range of the t i d e .  - 21 -  of the gauge and the area within a radius of about 1 mile of the gauge; - the methods by which elevations were o r i g i n a l l y established and have been maintained during the period of  operation;  - a chronological table showing the h i s t o r y of bench marks and t i d a l datum elevations; - a l i s t and d e s c r i p t i o n of bench marks used f o r reference;  and  - a tabulation of bench mark elevations.  A d e t a i l e d examination was made of these data. The following points emerged: 1) the s i t e s of the gauging stations have been altered in some instances, thus introducing u n c e r t a i n t i e s i n the order of l e v e l l i n g accuracy; 2) chart or t i d a l datum has been altered at some stations. However, since a datum i s established by d e f i n i t i o n and not by observation, t h i s does not a f f e c t values of DMSL; 3) annual l e v e l l i n g checks have not been c o n s i s t e n t l y recorded they may  although  have been c a r r i e d out. Where they were, however, the figures  show that since about 1940  the height difference between zero point of  the t i d e pole and bench mark remained constant  to + 3 mm  (0.01  f t ) at  the seven stations considered; 4) due to 3), the accuracy of any annual value of DMSL i s estimated to be not better than + 3 mm 5) although observations since about 1909,  (0.01 f t ) ; have been taken almost continuously  at most stations  parts of older records no longer e x i s t . This i s the  reason for the gaps i n the time-spans of a v a i l a b l e records shown in Table I  - 22 T a b l e IV. Time-spans o f a v a i l a b l e t i d a l r e c o r d s  Sta.No.  Location  168 169 170  Victoria F u l f o r d Harbour Vancouver  171  Point Atkinson  172  Tofino  173 175  A l e r t Bay P r i n c e Rupert  3.2.  Continuous r e c o r d to from  -  No. o f years  1909 1968 1953 m 1968 1923 1910 1943 1968 1919 1914 1947 — 1968 1910 1920 1943 1968 1948 • 1968 1909 1919 1943 mt 1968  60 16 14 26 6 22 11 26 21 11 26  -  Annual l e v e l l i n g checks recorded S i n c e 1941 All All All All A l l , e x c e p t 1952 A l l , e x c e p t 1910 All A l l , e x c . 1950,52 A l l , e x c . 1916-19 All  A n a l y s i s o f DMSL  3.2.1. S e a s o n a l v a r i a t i o n s o f DMSL The i n v e s t i g a t i o n o f s e a s o n a l v a r i a t i o n s c o n s i s t e d o f t h e f o l l o w i n g three steps: 1) M o n t h l y means o f DMSL and w e i g h t s a s s o c i a t e d w i t h them were computed and t a b u l a t e d f o r each  station:  The c o n v e r s i o n o f months and y e a r s i n t o d e c i m a l s o f a y e a r was a c h i e v e d by t h e f o r m u l a M - Y + ( N - 0.5)/12 , M  where M i s t h e t i m e i n t e r v a l i n y e a r s and d e c i m a l f r a c t i o n o f a y e a r between t h e y e a r 1900.0 and t h e m i d - p o i n t o f any month i n any given year t h e r e a f t e r , Y i s t h e y e a r number r e l a t i v e t o 1900.0, and Nj^ i s t h e number o f the month i n t h e y e a r Y. As an example, June 1948, f o r which Y « 48.0 and N^ - 6, i s r e p r e s e n t e d by t h e number 48.46. M o n t h l y means  were computed by t a k i n g t h e s i m p l  average o f a l l d a i l y means a v a i l a b l e i n t h e r e s p e c t i v e month. F i n a l l y a weight f o r each monthly mean was computed a c c o r d i n g t o t h e  - 23 formula W  where  M"V D' N  i s the weight associated with the monthly mean  ,  N. i s the number of d a i l y means a v a i l a b l e i n a given month M, and NQ  i s the number of days i n that month M.  The fact that February has 29 days in a leap year was taken into account both i n the computation of monthly means  and t h e i r weights  .  A sample computer output of the tabulation i s given i n Appendix 2 f o r s t a t i o n No. 173, ALERT BAY, B.C. 2) Employing the technique of least squares f i t , an appropriate regression was performed f o r each s t a t i o n . For a l l stations the regression function was chosen to be of the form  - a where Z  w  Q  + aj.M + A cos [zir/TCM - M )j , Q  i s a monthly value of DMSL, referred to Chart Datum, f o r the month M,  a  Q  represents a mean value of DMSL at 1900.0,  a^ represents a l i n e a r secular trend, M  i s the month i n decimals of the year Y,  A  i s the amplitude of the seasonal o s c i l l a t i o n ,  T  i s the period of the seasonal o s c i l l a t i o n , and  M  Q  i s i t s phase l a g .  No further sinusoidal terms were considered because the purpose was not to c a r r y out a harmonic a n a l y s i s but rather to determine the amplitude A, the period T and the phase lag M  of a suspected seasonal o s c i l l a t i o n . The  Q  term ajM was included to account f o r a possible secular trend at least l i n e a r l y . In view of the above, a , a p A, T, and M 0  Q  were introduced as co-  e f f i c i e n t s to be determined together with t h e i r standard errors (SE)  24 -  -  according to the method of least squares f i t . Most probable values f o r the f i v e c o e f f i c i e n t s and t h e i r standard errors were computed with the aid of a standard computer subroutine (LQF in UBC program l i b r a r y ) . The weights were taken into account. A sample computer output f o r ALERT BAY i s attached i n Appendix 3, The r e s u l t s , as f a r as they are relevant to t h i s subsection, are l i s t e d i n Table V.  Table V. Amplitude, period and phase lag of seasonal o s c i l l a t i o n  Sta.No. 168 169 170 171 172 173 175  Location Victoria Fulford Harbour Vancouver Point Atkinson Tofino A l e r t Bay Prince Rupert  Period 1909-68 1953-68 1943-68 1947-68 1943-68 1948-68 1943-68  n  *) A,SE(A),(cm) T,SE(T),(yrs)  709 190 310 260 308 247 312  8.3 7.3 5.6 5.1 12.2 10.8 10.7  + + + + + • +  0.4 0.7 0.5 0.6 0.6 0.6 0.6  1.0004 0.9972 1.0010 0.9988 0.9988 0.9978 0.9995  + + + + • + +  0.0004 0.0032 0.0020 0.0028 0.0010 0.0016 0.0012  M ,SE(Mj,(yrs) e  0.019 + 0.146 0.090 0.029 0.071 + 0.128 + 0.004 m  m  4 + + +  0.017 0.197 0.115 0.163 7 0.059 + 0.093 + 0.068  *) n « number of monthly means used  3) F i n a l l y f o r each s t a t i o n the monthly means as computed i n step 1 together with the respective regression function obtained i n step 2 were plotted on an automatic p l o t t e r using standard subroutines. The scale chosen f o r the horizontal (time) axis i s 1 year » 2 inches and f o r the v e r t i c a l (DMSL) axis 1 foot • 2 inches. Inspection of the p l o t s confirmed the computational r e s u l t s . For i l l u s t r a t i o n , the plot f o r ALERT BAY i s shown i n Appendix 4^.  3.2.2. Secular v a r i a t i o n s of DMSL S i m i l a r l y to the procedure i n the preceding subsection, several steps were taken i n the study of secular changes. 1) Yearly means of DMSL together with t h e i r corresponding weights were computed f o r each s t a t i o n :  5) Numbers such as, f o r example, 63.499 or 63.999 on the time axis are due to accumulation of round-off errors i n the computer and should be read as 63.5 or 64.0, r e s p e c t i v e l y .  . - 25 The annual means of DMSL were computed from monthly means using the formula _  z  jg  yj) y j )  where Zy i s an annual value of DMSL, referred to Chart Datum, f o r the year Y, Z (J)  i s the J  WJ^CJ)  i s the weight of t h i s monthly mean, and  M  N  T  H  monthly mean in the year Y,  i s the number of months f o r which observations are a v a i l a b l e in the year Y.  The difference between an annual value thus computed from monthly means as a weighted mean and an annual value computed from d a i l y means as a simple mean may  amount up to 1 mm  (0.003 f t ) due to round-off e r r o r s .  Compared to observational e r r o r s , t h i s computational error i s small and is negligible. The weights associated with annual means were computed from the formula  1  where W  Y  12  i s the weight of the given annual mean f o r the year Y.  Appendix 5 contains a computer l i s t i n g of a l l annual values of DMSL a v a i l a b l e and t h e i r weights for the seven stations considered. 2) For each s t a t i o n , a plot of the annual means was prepared. A horizontal scale of 1 year • 0.25  inch and a v e r t i c a l scale of 0.1  f t «• 1 inch  was  employed. The numbers on the time axes are placed at the mid-point of the year to which they correspond, e.g. 50.0  indicates the middle of the  year 1950. Annual values f o r consecutive years only were joined by straight l i n e s . Appendices  6 to 11 are the p l o t s so obtained, completed  regression l i n e s , to be discussed below.  by  - 26 3) The p l o t s were i n s p e c t e d . S i n c e t h e p a i r s o f s t a t i o n s VICTORIA and FULFORD HARBOUR, VANCOUVER and POINT ATKINSON a r e n o t t o o w i d e l y s e p a r a t e d  geo-  g r a p h i c a l l y , t h e y were p a i r e d and used f o r c o m p a r i s o n . i ) The s e m i - t r a n s p a r e n t  p l o t f o r FULFORD HARBOUR f o r t h e p e r i o d  1953-1968  was o v e r l a i d on t h a t f o r VICTORIA f o r t h e same p e r i o d . The c o m p a r i s o n r e v e a l e d a d i s t i n c t s i m i l a r i t y i n p a t t e r n f o r t h a t p e r i o d . The same i s t r u e o f VANCOUVER and POINT ATKINSON f o r t h e p e r i o d 1947-1968. F o r t h e s e 22 y e a r s t h e r o o t mean square d i f f e r e n c e amounts t o + 1.2 cm ( 0 . 0 4 f t ) . R e t a i n i n g the r e l a t i v e p o s i t i o n o f the p l o t s and hence t h i s  close  agreement f o r the p e r i o d 1947-1968, a r o o t mean square d i f f e r e n c e o f + 6.6 cm (0.22 f t ) i s o b t a i n e d  f o r t h e p e r i o d 1914-1922.  i i ) The y e a r l y v a r i a t i o n p r i o r t o 1920 i s c o n s i d e r a b l y g r e a t e r than t h a t s i n c e about 1940. T h i s d e c r e a s e i n v a r i a t i o n h o l d s f o r s t a t i o n s VANCOUVER, POINT ATKINSON, TOFINO and PRINCE RUPERT. A t T0FIN0, f o r i n s t a n c e , t h e maximum v a r i a t i o n i n t h e p e r i o d 1914-1920 amounts t o 19 cm (0.62  f t ) , w h i l e from 1943 t o 1968 i t i s o n l y 12 cm ( 0 . 4 0 f t ) .  These f i n d i n g s , i n c o n j u n c t i o n w i t h t h e bench mark i n f o r m a t i o n a v a i l a b l e , l e d t o t h e c o n c l u s i o n t h a t r e c o r d s p r i o r t o about 1940 a r e n o t s u f f i c i e n t l y accurate  and a r e t h u s n o t s u i t a b l e f o r c o m p u t a t i o n o f a r e g r e s s i o n  VICTORIA i s an e x c e p t i o n  line.  s i n c e o b v i o u s l y t h e gauge was o p e r a t e d c a r e f u l l y  and r e c o r d s were p r o c e s s e d  properly.  4) U s i n g o n l y t h o s e r e c o r d s which a r e s u i t a b l y r e l i a b l e , r e g r e s s i o n l i n e s were computed f o r each s t a t i o n i n o r d e r t o d e t e r m i n e t h e s e c u l a r v a r i a t i o n . S i n c e no m e t e o r o l o g i c a l d a t a were a v a i l a b l e and s i n c e t h e i n f l u e n c e o f t h e nodal  t i d e i s n e g l i g i b l y s m a l l f o r p e r i o d s o f about 19 y e a r s o r m u l t i p l e s  o f i t , o n l y t h e f i r s t term o f R o s s i t e r ' s e q u a t i o n For a l l seven s t a t i o n s l i n e a r r e g r e s s i o n e q u a t i o n s  Z  y  - a  Q  + a  l  Y  (page 17) was u s e d . ( p - 1)  27 and q u a d r a t i c r e g r e s s i o n e q u a t i o n s ( p -  a  + aY  + a Y  {  D  2)  2  2  were computed. A c u b i c e x p r e s s i o n ( p • 3) was n o t c a l c u l a t e d because t h e p l o t s r e v e a l e d no e v i d e n c e  at a l l o f a c u b i c law o f change. E s t i m a t e s  o f the r e g r e s s i o n c o e f f i c i e n t s a , a a and t h e s t a n d a r d e r r o r s o f t h e s e 1» 2 o e s t i m a t e s were computed by the method o f l e a s t squares w i t h t h e a i d o f a  t h e computer s u b r o u t i n e LQF. one was  0  A q u a d r a t i c law o f change as w e l l as a l i n e a r  accepted o n l y i f the standard e r r o r of a  2  d i d n o t exceed  the  a b s o l u t e v a l u e o f a^ . I n June 1946 a s e v e r e earthquake  w i t h i t s e p i c e n t r e near or at the c e n t r e  o f t h e e a s t c o a s t of Vancouver I s l a n d was r e c o r d e d and became known as t h e B r i t i s h C o l u m b i a E a r t h q u a k e (Hodgson, 1946). I n o r d e r t o d e t e c t p o s s i b l e e f f e c t s of t h i s earthquake, puted  two a d d i t i o n a l r e g r e s s i o n e q u a t i o n s were com-  f o r VICTORIA f o r the p e r i o d s 1909-1945 and  1947-1968. A l s o , t o g i v e  a b e t t e r c o m p a r i s o n w i t h POINT ATKINSON, an a d d i t i o n a l r e g r e s s i o n was  per-  formed f o r VANCOUVER f o r the p e r i o d 1947-1968. A p p e n d i c e s 6 t o 11 show the r e g r e s s i o n l i n e s together w i t h the o r i g i n a l o b s e r v a t i o n s . 5) An F - t e s t was used t o t e s t the s i g n i f i c a n c e o f t h e c o e f f i c i e n t a^ i n the r e g r e s s i o n equation it  z  y ™ o a  +  a  l  Y  *  I n  s  t  a  n  d  a  r  d  t e x t b o o k s on  statistics  i s shown t h a t i f t h e o b s e r v a t i o n s a r e N o r m a l l y d i s t r i b u t e d , t h e  ratio  F(l,N-2) SE(a,) f o l l o w s t h e F - d i s t r i b u t i o n w i t h 1 and N-2 case o f weighted  d e g r e e s o f freedom ( i n t h e  o b s e r v a t i o n s N i s e q u a l t o t h e sum o f t h e w e i g h t s ) . U s i n g  the above f o r m u l a , a v a l u e o f F and the p r o b a b i l i t y a s s o c i a t e d w i t h  - 28 -  t h i s value were computed. The p r o b a b i l i t y i s that of obtaining an F - value greater than or equal to the one c a l c u l a t e d , given that (3 • 0 i n the "true" regression equation  Z  - « + (JY . I f t h i s p r o b a b i l i t y i s l e s s than 0.05,  Y  one may u s u a l l y conclude that a^ i s s i g n i f i c a n t l y d i f f e r e n t from zero. In other words, the trend i s s t a t i s t i c a l l y s i g n i f i c a n t at the 95% p r o b a b i l i t y l e v e l . A sample computer output of a l i n e a r regression and the test of s i g n i f i c a n c e i s shown in Appendix 12 f o r ALERT BAY. The relevant findings |a l f o r a l l  of steps 4 and 5 are summarized in Table VI (Since SE(a ) >  2  2  stations except VICTORIA, a, i s given f o r VICTORIA o n l y ) .  Table VI. Table of regression c o e f f i c i e n t s  Sta.No. 168  Location  Period  Victoria  169 170  Fulford Harbour Vancouver  171 172 173 175  Point Atkinson Tofino A l e r t Bay Prince Rupert  a SEUj) (mm/yr) p  n*> 1909-68 1909-68 1909-45 1947-68 1953-68 1943-68 1947-68 1947-68 1943-68 1948-68 1943-68  60 60 37 22 16 26 22 22 26 21 26  •  + + + + + +  1.20 0.61 0.12 1.27 1.49 2.65 1.92 2.10 0.46 0.30 2.90  + 1.18 + 0.24 + 0.51 + 0.89 +1.65 + 0.64 + 0.86 + 0.82 7 0.76 + 1.01 + 0.79  ?2», £ 2 > (mm/yr'') S E  a  F-Prob. for a^  + 0.023 + 0.015 0.01 0.80 0.17 0.39 0.00 0.04 0.02 0.56 0.76 0.00  *) n • number of annual means used  3.3. Discussion of r e s u l t s In order to interpret the r e s u l t s , one f i r s t has to make an assumption about the influence of factors (9) to (13), i n c l u s i v e , on,DMSL. One may assume that t h e i r influence on a monthly and/or annual value of DMSL does not exceed + 3 mm (0.01 f t ) . Based on t h i s assumption, which means that DMSL and PMSL do not d i f f e r by more than 3 mm, one may now interpret changes i n DMSL p h y s i c a l l y as changes i n PSL or PMSL.  - 29 -  Seasonal v a r i a t i o n s (changes i n PSL) can be expressed numerically i n terms of the amplitudes of the seasonal o s c i l l a t i o n (Table V, c o l . 5 ) . A minor part of t h i s amplitude i s due to the solar annual t i d a l constituent Sa (about 1.2 cm, see factor (1)) but the greater part of i t i s due to meteorological e f f e c t s (factor ( 2 ) ) . The amplitudes range from about 5 cm (0.15 f t ) at POINT ATKINSON to about 12 cm (0.39 f t ) at TOFINO. This difference i n amplitudes at the stations must be considered i n conjunction with t h e i r geographic positions, and consequently, with d i f f e r e n t influences of barometric pressure and p r e v a i l i n g winds. I t i s not s u r p r i s i n g that the greatest amplitude i s encountered at TOFINO which i s d i r e c t l y exposed to the P a c i f i c ocean. Correspondingly the smallest amplitudes are found at VANCOUVER and POINT ATKINSON, both of which are sheltered by Vancouver Island and the San Juan Islands. Since one may assume that a i r pressure i s f a i r l y well constant over about 250 km (150 mi), t h i s r e s u l t i s c l e a r l y i n d i c a t i v e of the great influence of p r e v a i l i n g winds on PSL. The periods (Table V, c o l . 6) are approximately 1 year, but the fact that t h e i r standard errors are greater than t h e i r deviation from 1.0000 (except for TOFINO and ALERT BAY) seems to indicate a period of exactly 1 year. A s i m i l a r conclusion can be drawn from the phase lags of the seasonal o s c i l l a t i o n (Table V, c o l . 7). Their signs vary between the stations and t h e i r standard errors are of the order of t h e i r magnitude or even exceed i t . I t may therefore be concluded that on the average the maximum value of the seasonal o s c i l l a t i o n coincides with a t r a n s i t i o n to a new year.  Secular v a r i a t i o n s (changes i n PMSL) are expressed i n terms of the regression c o e f f i c i e n t s a^ and} a  2  l i s t e d in Table VI, c o l . 5,6. Each of the three  regression equations computed f o r VICTORIA shown i n that table and i n the p l o t s (Appendices 6,7) has c e r t a i n  advantages:  - 30 1) The computation of a single l i n e a r regression equation for the entire period 1909-1968 permits performance of a test of s i g n i f i c a n c e for a^ and allows the mean rate of change to be expressed by the single figure » + 0.6 mm/yr with SECa^ « + 0.2 mm/yr . 2) The computation of two l i n e a r regression l i n e s f o r the periods 1909-1945 and 1947-1968 makes allowance  f o r the possible d i s c o n t i n u i t y i n land  movement caused by the B r i t i s h Columbia Earthquake of 1946. As shown i n Appendix 6, the "jump" i n 1946 amounts to 1.2 cm (0.04 f t ) and may be due to a sudden r e l i e f of the earth's c r u s t , although nothing d e f i n i t e can be stated because of the r e l a t i v e l y large yearly v a r i a t i o n . The trends themselves indicate emergence from 1909 to 1945 and submergence from 1947 to 1968, but they are not s t a t i s t i c a l l y s i g n i f i c a n t . 3) The computation of a quadratic regression l i n e f o r the period 1909-1968 provides a more f l e x i b l e continuous description of the geophysical processes involved than does a straight l i n e . Quadratic regressions should always be considered f o r periods longer than 30 years. For a l l other s t a t i o n s , l i n e a r trends were most s u i t a b l e . The trends are s i g n i f i c a n t f o r VICTORIA (1909-1968), VANCOUVER (1943-1968), POINT ATKINSON (1947-1968) and PRINCE RUPERT (1943-1968). At a l l these stations a p o s i t i v e secular v a r i a t i o n i s observed, thus indicating submergence. Since submergence (as well as emergence) characterizes only a r e l a t i v e movement between PMSL and land, an attempt i s made to separate the components of submergence. In doing so, use i s made of the following d e f i n i t i o n s :  Relative movement (RM)  + Submergence  Sea l e v e l movement (SLM)  + Emergence  Rise  Fall  Land movement (LM)  + Uplift  •a  Subsidence  - 31 Based on these d e f i n i t i o n s , the three movements can be related by the equation RM - SLM - LM . Solving f o r LM y i e l d s LM - SLM - RM . In the l a t t e r equation the rate of RM i s known from the regressions computed above ( c o e f f i c i e n t a,). The rate of SLM i s assumed to amount to +1.0 mm/yr ( e u s t a t i c r i s e of PMSL; see factor ( 7 ) ) . The standard  error of  t h i s rate i s estimated to be + 0.3 mm/yr (Montag, 1970). Considering the four above-mentioned stations with s t a t i s t i c a l l y s i g n i f i c a n t the rates of movements as computed from the r e l a t i o n  only  trends,  LM - SLM - RM are  l i s t e d in Table VII together with estimates of t h e i r standard  errors.  Table VII. Rates of PMSL, r e l a t i v e and land movement Sta.No.  Location  168 170  Victoria Vancouver  171 175  Point Atkinson Prince Rupert  Period  SLM (mm/yr)  RM (mm/yr)  LM (mm/yr)  1909-68 1943-68 1947-68 1947-68 1943-68  + + + + +  + + + + +  + -  1.0 1.0 1.0 1.0 1.0  + + + + +  0.3 0.3 0.3 0.3 0.3  0.6 2.6 1.9 2.1 2.9  + + + + +  0.2 0.6 0.9 0.8 0.8  0.4 1.6 0.9 1.1 1.9  + + + + +  0.4 0.7 0.9 0.9 0.9  Only vague statements can be made about the causes of the land movements given i n the last column of the above table: Probably the cause of land u p l i f t at VICTORIA and subsidence at VANCOUVER, POINT ATKINSON and PRINCE RUPERT i s of tectonic origin,although the p o s s i b i l i t y of l o c a l atectonic movements cannot be excluded. Geological studies (Mathews et a l . , 1970) have shown that i n southwestern B r i t i s h Columbia i s o s t a t i c adjustment a f t e r deglaciation ( f a c t o r (5a)) was e s s e n t i a l l y complete about 8000 years ago. Tectonic movements due to sedimentation may also be disregarded  6) This separation i s made possible only by assuming an e u s t a t i c r i s e o f PMSL at a c e r t a i n r a t e . Should new studies of world-wide changes i n PMSL r e s u l t in a better f i g u r e f o r SLM, the new f i g u r e would obviously d i r e c t l y a f f e c t the rates of land movement shown i n the l a s t column of Table VII.  - 32 because of t h e i r slow rate ( f a c t o r ( 5 c ) ) . It i s thus concluded that the land u p l i f t at VICTORIA and the land subsidence at VANCOUVER, POINT ATKINSON and PRINCE RUPERT i s due to orogenesis ( f a c t o r (5b)), provided no atectonic movements have taken place. Further geological studies should c l a r i f y t h i s matter.  CONCLUSION  Causes and e f f e c t s of seasonal and secular changes i n sea l e v e l were covered i n section 2 a f t e r d e f i n i t i o n s of sea l e v e l were given in the f i r s t section. The main causes f o r seasonal v a r i a t i o n s of PSL were found to be barometric pressure and p r e v a i l i n g winds. Tectonic movements of the earth's crust and eustatic changes in PMSL are the main reasons f o r secular v a r i a t i o n s i n PMSL. In general the factors influencing sea l e v e l are of widely d i f f e r e n t o r i g i n and t h e i r study involves most of the geo-sciences such as hydrography, oceanography, climatology, meteorology,  geology, geodesy, and, of course,  astronomy. Obviously the problems associated with sea l e v e l can be solved s a t i s f a c t o r i l y only by international cooperation of a l l branches of sciences named. The formation of the "IAG - Special Study Group 2.22"  (International  Committee f o r Mean Sea Level) in 1960 was a f i r s t step toward the achievement of  t h i s goal. The recent "Symposium on Coastal Geodesy" held by t h i s group  (Munich 1970) was another attempt to r e a l i z e international and  interdiscipli-  nary cooperation. As f a r as possible the r e s u l t s of t h i s meeting were taken into account in t h i s t h e s i s . Section 3 described the numerical determination of seasonal and secular v a r i a t i o n s i n sea l e v e l on the coast of B r i t i s h Columbia. The seasonal v a r i a t i o n can be regarded as an o s c i l l a t i o n with a period of about 1 year, the maximum height of t h i s o s c i l l a t i o n coinciding with the t r a n s i t i o n to a new The average amplitude of t h i s annual o s c i l l a t i o n f o r seven stations on the  year.  - 33 -  B r i t i s h Columbia coast amounts to about 9 cm (0.3 f t ) . At TOFINO the o s c i l l a t i o n has the greater amplitude (12 cm or 0.4  f t ) and i s smallest at POINT ATKINSON  (5 cm or 0.15 f t ) . Secular changes i n PMSL were determined as linear trends of submergence and/or emergence. At VICTORIA, the secular v a r i a t i o n can also be  represented  by means of a quadratic regression l i n e . Except at ALERT BAY (1948-1968) and VICTORIA (1909-1945) submerging conditions are found. The B r i t i s h Columbia Earthquake i n 1946 may  have resulted in a sudden land subsidence of 1.2  cm  (0.04 f t ) at VICTORIA. Excluding stations having non-significant trends, the remaining  trends of submergence were segregated  into movements of sea l e v e l  and movements of land,assuming an eustatic r i s e of sea l e v e l at a rate of 1.0 mm/yr. There are d e f i n i t e subsidences of land at VANCOUVER, POINT ATKINSON and PRINCE RUPERT during the l a s t 20 years due to tectonic (or atectonic) movements and since 1909,  a probable  land u p l i f t at VICTORIA.  F i n a l l y , a few recommendations and suggestions are provided which hopefully w i l l be u s e f u l h i n t s for further observations and studies; 1) More permanently operated  t i d e gauge stations should be established  along the coast of B r i t i s h Columbia. When s e l e c t i n g s i t e s f o r a d d i t i o n a l s t a t i o n s , geophysic By 1967,  as well as hydrographic  aspects should be borne i n mind.  14 permanent s t a t i o n s were already i n operation, but t h i s i s s t i l l  too small a number on which to base d e f i n i t e conclusions about v e r t i c a l movements of greater coastal areas. 2) The basic reference f o r DMSL at any s t a t i o n should be a t i d e gauge bench mark (T.G.B.M.), connected to several a d d i t i o n a l bench marks in the v i c i n i t y , but not included i n the national l e v e l l i n g net and i t s adjustments. L e v e l l i n g between T.G.B.M. and the n a t i o n a l net then may  give  evidence  of l o c a l land movement, but the basic information about DMSL should always be recoverable. It i s the p r a c t i c e of the "Canadian Hydrographic Service"  - 34 -  to use T.G.B.M. as a basic datum (although c a l l e d Chart Datum) and t h i s practice  should not be  altered.  3) Tide gauge bench marks should be set according to geodetic  standards  and i n a manner which assures t h e i r permanent existence over decades. In questionable cases a geodesist should be consulted. 4) L e v e l l i n g between tide gauge bench mark and gauging device or devices should be c a r r i e d out every s i x months with an accuracy of + 0.5  to 1.0  mm/Vkm , and the r e s u l t s should be c a r e f u l l y recorded. 5) Meteorological data such as a i r pressure, wind v e l o c i t y and  direction  and temperature should be recorded ( i d e a l l y at each gauge station) i n addition to t i d a l data,in order to permit a more complete evaluation of the mathematical model proposed by Rossiter. 6) Further attempts should be made to determine the amplitude and the phase lag of the nodal t i d e .  - 35 -  BIBLIOGRAPHY Dohler, G. (1965). Hydrographic t i d a l manual. Special publication of the Canadian Hydrographic Service, Ottawa. Doodson, A.T. (1921). The harmonic development of the tide-generating p o t e n t i a l . Proc. Roy. Soc. London, A 100, 305-329. Fairbridge, R.W. (1961a). Convergence of evidence on c l i m a t i c change and ice ages. Ann. N.Y. Acad. S c i . , v o l . 95(1). Fairbridge, R.W. (1961b). Eustatic changes i n sea l e v e l . In Physics and Chemistry of the Earth, v o l . 4, Pergamon Press. Fairbridge, R.W. (1962). World sea l e v e l and c l i m a t i c changes. Quaternia, Rome, v o l . 6, 180-193. Gutenberg, B. (1941). Changes i n sea l e v e l , p o s t g l a c i a l u p l i f t , and m o b i l i t y of the earth's i n t e r i o r . B u l l . Geol. Soc. Am., v o l . 52, 721-772. Haubrich, R.Jr. and W.H. Munk (1959). The pole t i d e . J . Geophys. Res., v o l . 64, 2373-2388. Hicks, S.D. and W. Shofnos (1965). The determination of land emergence from from sea l e v e l observations i n south-east Alaska. J . Geophys. Res., v o l . 70, 3315-3319. Hodgson, E.A. (1946). B r i t i s h Columbia Earthquake. J . Roy. A s t r . Soc. Can., v o l . 40, 285-319. K a l l e , K. (1945). Der Stoffhaushalt des Meeres. Probl. d. kosm. Phys., v o l . 23, Leipzig. Kuenen, Ph.H. (1955). Sea l e v e l and c r u s t a l warping. Geol. Soc. Am., Special paper 62. L i s i t z i n , E. and J.G. P a t t u l l o (1961). The p r i n c i p a l factors influencing the seasonal o s c i l l a t i o n of sea l e v e l . J . Geophys. Res., v o l . 66, 845-852. Mathews, W.H. et a l . (1970). P o s t g l a c i a l c r u s t a l movements i n southwestern B r i t i s h Columbia and adjacent Washington state. Can. J . Earth S c i . , v o l . 7, no. 2, 690-702. Munk, W.H. and R. Revelle (1952). On the geophysical interpretation of i r r e g u l a r i t i e s i n the rotation of the earth. Mon. Not. R. A s t r . Soc. Geophys. Suppl. 6, 331-347. P a t t u l l o , J.G. (1963). The sea, v o l . I I : Seasonal changes i n sea l e v e l . New York, Interscience. R o s s i t e r , J.R. (1962). Long-term v a r i a t i o n s i n sea l e v e l . In ( H i l l , M.N. editor) The sea, v o l . I, New York and London, John Wiley and Sons, Inc.  - 36 Rossiter, J.R. (1967). An analysis of annual sea l e v e l v a r i a t i o n s i n european waters. Geophys. J . R. A s t r . S o c , v o l . 12, 259-299. Valentin, H. (1952). Die Kuesten der Erde. Petermanns Geographische Mitteilungen, Ergaenzungsheft 246.  Selected papers presented at the "Symposium on Coastal Geodesy", Munich 1970: Ku, L.F. (1970). The spectra of mean sea l e v e l s along Canadian coast l i n e s . Montag, H. (1970). On the accuracy of determination of secular v a r i a t i o n s of mean sea l e v e l at the B a l t i c Sea coast. Wemelsfelder, P.J. (1970). Mean sea l e v e l as a fact and as an i l l u s i o n .  APPENDIX 1 Sample l i s t i n g of d a i l y means of DMSL for ALERT BAY, B.C. ( 1967)  DAY  MONTH  MONTHLY MEAN  DAILY MEAN LEVELS  01 10 11 20 21 31  1 67 1 67 1 67  NO 173 ALERT BAY B C 912 937 928 947 970 989 963 958 978 1065 1048 1028 1003  01 10 11 20 21 28  2 67 2 67 2 67  NO 173 ALERT BAY B C 1018 999 991 950 990 990 943 890 888 919  01 10 11 20 21 31  3 67 3 67 3 67  01 10 11 20 21 30  DAY  914 975 1001  877 908 1012  890 907 1042  917 955 1067  936 1072 1052  PST 965 1081 998  963 974 964  914 965 928  906 952 922  901 968 951  945 902 957  942 883  PST 924 907  NO 173 ALERT BAY B C 946 924 923 926 935 958 960 978 1041 1036  904 971 964  894 1002 960  874 1039 961  883 1015 959  930 1003 976  936 1009 967  PST 940 1019 954  4 67 4 67 4 67  NO 173 ALERT BAY B C 928 920 930 956 973 970 919 912 889 933  945 946 892  929 958 902  901 967 927  910 947 949  921 961 957  921 953 941  PST 926 925 916  01 10 11 20 21 31  5 67 5 67 5 67  NO 173 ALERT BAY B C 916 916 917 916 897 893 907 879 879 889  909 888 882  891 892 877  886 920 913  894 908 933  912 893 962  934 888 950  PST 932 903 937  01 10 11 20 21 30  6 67 6 67 6 67  NO 173 ALERT BAY B C 926 950 947 920 921 902 916 905 903 896  938 898 908  937 904 918  917 922 920  903 930 914  912 931 903  918 935 893  PST 912 920 888  7 67 7 67 7 67  NO 173 ALERT BAY B C 894 891 923 891 903 892 904 891 894 896  925 898 896  920 910 897  909 914 902  899 923 916  897 914 923  888 913 918  PST 889 896 913  907  01 10 11 20 21 31  8 67 8 67 8 67  NO 173 ALERT BAY B C 897 898 905 917 918 921 910 915 909 897  899 926 880  895 922 903  892 918 928  877 896 931  876 869 943  901 875 936  PST 923 930 949  977  01 10 11 20 21 30  9 67 9 67 9 67  NO 173 ALERT BAY 8 C 983 929 908 966 926 913 939 951 911 927  915 916 953  920 917 930  909 932 935  931 925 963  969 902 962  969 924 973  PST 1004 942 964  01 10 11 20 21 31  10 67 10 67 10 67  NO 173 ALERT BAY B C 978 975 961 996 955 960 961 1010 1010 933  951 882 994  973 889 944 „  997 882 958  1009 930 1032  1022 929 966  1007 909 920  PST 1034 960 938  01 10 11 20 21 30  11 67 11 67 11 67  NO 173 ALERT BAY B C 862 873 910 944 944 951 944 937 935 940  943 974 934  968 936 885  986 926 873  984 966 915  1007 937 955  1012 919 980  PST 1022 923 966  01 10 11 20 21 31  12 67 12 67 12 67  NO 173 ALERT BAY B C 998 1044 1068 1086 912 877 862 865 955 947 980 949 932  1061 904 932  1068 917 910  1049 954 891  1007 948 868  1023 938 881  PST 988 931 898  01 10 11 20 21 31  1001  938  918  HR  HIGH HT  DAY  HR  LOW HT  27 1340  1810  9 1905  137  24 1246  1708  25 2034  97  28  232  1785  28  905  205  26  151  1734  26  845  62  "24  32  1702  25  852  15  22  20  1667  23  836  77  21  13  1592  21  739  119  129  1610  7  838  117 ! 00  8 1559  1651  4  719  172  Table 1 - Dally Mean Levels These tables contain the daily mean level, the monthly mean level and the Instantaneous extreme levels recorded each month. The days of the month are listed ln the first two columns, e.g., 01-10 Indicates that the line contains the data for the first to the tenth days. The next two colun give the month and year. The centre block contains dally mean levels computed from hourly readings. The means are computed to thousandths of a foot and are rounded off to the nearest hundredth of a foot, e.g., 60011 Is 600.11 feet and 1439 Is 14.39 feet. On the left of the central block Is a column of monthly means, which are the average of the dally means available, and on the right under "Highs" and "Lows" are the day, time, and height of the monthly instantaneous extremes.  APPENDIX 2 Sample l i s t i n g of monthly means of DMSL f o r ALERT BAY, B.C. (1948 - 1968)  r N C 1 7 3 A L E R T E AY MCNTH AS.46 MMEAN 9.27 WEIGHT . 1 .OQ  ^  B  C  4 8.54 9.20  1.00  48 .63 9.26 1.00  48.71 .. 34 c  1.00  48.79 9.29 1 .00  48 .88 9.48 1.00  r 173 A L E R T - E A Y a c MONTH 49.13 MMEAN 9 . 81 9.10 WEIGHT 1.00 l.CC  49.21 9.68 1.00  173 A L E R T B A Y B C 50.04 50.13 MONTH 9.41 9.72 l.CC 1.00  5C.21 9 .69 l.OC  WEIGHT  N C 173 MCNTH MNEAN WEIGHT  N C 173 MONTH . NMEAN WEIGHT  NC :  49. 62 "9*0.2". 9.27 1 .00.' 1 .00  4 9.71 9.25 1 .00  49.79 9.02 1.00  49.fi? 9.73 LOG  49.96 9.49 1.00  "50 .l9" 50.3 8 .'. 50; 63 9.41 9..2 0 8 .97 1.00 l.OC ' ' • 1.00'fc.fW*^'; 1.00  50.71 9.18 1.00  50.79 9.85 1.00  50.88 9.79  50.96 10. 06 LOO  49.29 9.31 1. 00  NO  '^•"r  49.38 9.32 1.00  49.46 9.08 1.00  BAY  51.04 9.76 •1. C C  ALERT  BAY  52.04 10.14 1.00  B  !  1.00  !u'  C  51 . 13 9.73 1. CO  B  49.54  r  n'if'') ALERT  vvi..oc •' jj'^V ' •  NC  #*v.'  ,48.96V 9.75  51.21 9.27 • 1.00  5 1.29 ~ 5 T 7 I 7 9.00 9.23 1. CO 1 .00  _  51.46 9.06  1.00  51. 54 9.21 1.00  51. 63 9. 10 1 .00  51.71 9.27  1.00  51.79 9.5 5 1.00  51 .88 ' T f . 9 6 9.68 9.92 1.00 1 .00  C  52.13 52.21 9.76 , 9.47 1.00 l.CC  17 3 A L E R T B A Y B C 53.04 ' 53.13 ' 9 .3.5 10.28 1.00. 1.00  MONTH •MMEAN WEIGHT  5 3.21 9.51-  1.00  52. 29 9.21 1.00  52.38 '9.05 1 .00  52.46 9.15 1 .00  52.54 9.04 1 .00  52 .63 9. 2C '1.00  5.2 . 71 9. 21 1 .OC  52.79 9. 15 1.00  52.87 9.45 l.CC  52.96 1C.36 l.CC  5 3. 29 9.27  53.38 9.42 l.OC  53.46 9.18 1 .00  53.54 9.16 1.00  53.63 9. 30 l.OC  .53.71 9.30 l.OC  53.79 9. 49 1.00  53.88 10.16 1 .CC  5 2.96 9.68 1.00  54.71 9.30 l.OC  54.79 9. 50  54.88 9 .98  1.00  54 .96 10.10 1. CO  55.63 8. 9l.OC  55.71 9.07 l.OC  55.79 9.37 l.CC  55. 86 9.51 l.CC  55.96 9 .96 1.00  56.46 56 .54 9. 34' -, .9.10 l.p:0.'  56.63 ' 9.05 l.'OC  56.7 1 9.12 l.OC  56.79 9.43 l.CC  56.86 9.08 l.CC  56.96 9 .48 1-00  5 7.46 9.24 I.CO  57. 6 2 9.31 1. O C  57.71 9.40 l.CC  57.79 9.49 l.CC  57.86 9.47 l.CC  57. 96 10.14 l.CC  i.co  •  N C 173 MONTH MNEAN WEIGHT  ALERT  EAV  54. 04 10.0 6 1.00'  e c 54 .13 10 .01 1 .00  173 A L E R T E A Y e c MONTH 55.04 55.13 9.64 MMEAN 1.00 WEIGHT 1 .00  54.21 9.44 1.00  54.29 ^.25 1.00  54.38 9.15  1.00  54.46 9.4 2 1.00  54.54 9. 23 1 .oo-  54.62 9.2C • '1.00  1.00 •  I'  NC  55.29 55.21 9.02 ~~ S.42 1 .00 1.00  55.38 8.90 1 .00  55.46 9.05 1.00 '••'...  N C 173 MONTH MMEAN WEIGHT  ALERT  N C 173 MONTH MMEAN WEIGHT  ALERT  E AY  56.04 10.22 1.00  e c 56. 12 9.45 1.00  56.21 ~5T.~29" ' 9.4 5 S. 16 1 .00 ' i . c o  5.6.38  55.54 9.15  1.00  .  • ,r  E AY  57.04 9.26 1 .00  e c 57.13 9.39 1 .00  57.21. 9. 58 .1.00  :  .. 25 1.00  c  57. 3^8 9.41 1 vOC  57.54 9.26 1.00  Nt 173 ALERT E AY B c MONTH 58 .04. • 5 8.13 MMEAftf 10 .20 10. 4 7 WEIGHT 1 .00 1 •CO  5 8.,21 9.65 1 .00  .58 .46 9.32 1 .00  58 .54 9 . 16 1 .CO  58. 63 9.32 1. O C  58.71 9.45 LOO  58. 79 9. 56 1. CO  58. 88 9.63 1. CG  58 .96 9 .92 1 .00  59.38 9.11 1 .00  59.46 9.27 1 .00  59 .54 9. 0 0 1 .00  59. 63 9. 11 1. OC  59.71 9.44 1.00  59. 79 9. 33 1. GC  59. 8 8 9.20 1. OC  59 .96 9 .66 1 • CO  60.38 9.46 1.00  60.46.  60 .-64  60.63 9.11 l.CO  60.71 9.03 l.CO  60. 79 9.36 l.CO  60.8 7 9.65 1 .CC  6C. 96 9.67 1.00  61.71 9 .10 1.00  61.79 9.18 1.00  61.8 8 9.35  1.00  61.96 9.54 1.00  62.79 9.79 l.CO  62.88 9.90 1.00  62.96 9.88 LOO  63.71 9.57 1.00  6 3. 79 9.90  63.88  1.00  63.96 9.86  1.00  1.00  64.71 9.13 l.CO  64. 79 9.25  5 8.29 58.38 c 59 9.16 1 .00. - 1.00 '•"  NC 173 ALE Ft E AY e c 59. 13 MONTH . •'A.. .04 59 MMEAN 10 . 0 2 9. 81 KE I'GHT;'. 1.00 .-.00 ,i ;  ,A^..NC  1 7 3  ~-V«W*T;  "-»-  ALERT.  -  V  "  E A Y „B C  60. C*?  . WEICHT  NC 173 MCNTH  68.13 60.21 9.6 6 9.46 1.00 .1 .00  9.73 1 .00  >!^V>';MMEAN  59:21" 5 9.29 9 . *&• v c;.15 1 .00" ;'-'\\ 00  ALERT  BAY  1.00 V  8.198  1  1.00  A  i 61.63 9.17  61 .29 9.17 1.00  61.38 9.25  NC 173 ALERT BAY B C KChTH 62.04 62.13 62.21 MMEAN . ;9. 33 9. 67 9.26 HEIGHT 1.00 l.CC LOG  62.29 9.12 LOG  62.38 62.46 9.03 8.98 l.CC 1.00  . . 62.54 62.63 62.71 8.94 9.'26 ' 9.31 l.CC l.CC 1.00  NO 173 ALERT BAY 8 C MC NT H 63.04 63 .13 MMEAN 9. 19 9. 90 WEIGHT LOO 1.00  6 2.29 S.68 l.GG  63.38 9.39 l.GG  63.54 9 .30 l.GG  WEIGHT  1.00  63.21 9.34 1 .00  61.46 9.19 1.00  61.54 9.07 l.CC  61 .21 10.03 1.00  MMEAN  6.1. C4 9. 99  8 C 61.13 10. 04 1.00  60.29 9. 53  1.00  6 3,46 9.15  1.00  . L O G  6 3.63 9.17 LOG  10.11  * >  •  ,  ?»>• " •••,U-  NO 173 ALERT BAY 8 C KG NTH 64.04 64. 13 MMEAN ' 10. ].5 9. 04 WEIGHT l.CC 1.00  64.21 9.22 LOG  6 4.29 8.83 1..C0  NC 173 ALERT BAY B C MONTH 65.04 6.5 .13 r MMEAN 9.74 {/9>.35  65.21 .9.13  65.2~9 . .65.38  wE  1  GH  VrJ'J  1*  c 0  .l.CC L O G :  1  9.36  i.ec  64.46 64.5 4 9.14 ' 9.21 1.00 1.00  64.38 8.90 LOG  ^  -f^%  6 5."4^F^v54 8...9^4,'.^.07 8...?^'..;^s?.07  8.87/..  1.00  6 5.63  9.29  1. i.#-SHilbo G^-''i^.op 1.00  NC 173 ALERT BAY B C MCNTH 66.04 66 .13 NKEAN 9.89 9.63 WEIGHT 1.00 ' -1 .OC  66.21 6 6.29 66.3.8;.. 66.46 9.65 9.02. 8.82 l . C C .-,1.CC l.'CG .' 'L'V:00  NC 173 ALERT BAY B C MCNTH 67.04 67.13 MMEAN 9.78 9.43 WE IGHT l . C C -LOG  ____. 67.21 6 7.29 '6,773 8 ~67.46 9.60 .9.33 9.07 9.16 1.00 l.CC r.OO. 1.00  :  64. 63 9.22 1.00  :,  66. 54 9.17 'l'.OQ  ;  1.00  64.88 9.51 1 .00  64.96 9.83  1 .00  ' 6 5.71 65.79 65.88 65.96 9.12 9.59 10.04 10. 04  1.00  1.00  1.00  1.00  66. 6 3 9. 1.1 1.00  66.71 66.79 9.25 9.26 1.00 1.00  66.88 9.62 LOO  66.96 10.09 1.00  67.63 9. 10 .1.00  67.71 9.3S 1.00  67.88 9.44 1.00  67.96 9.55 1.00  :  67.54 9.05 1 .00  67.79 9.61 1.00  NO 113 ALERT BAY B C KMh 68.04 .68 .13  MMEAN  9.81  9-84  WEIGHT  l.OC  1.00  68.21  9.72  1.00  66.29 8.95 l.OC  68.26 9.13 1.00  68.46 9.00 1.00  68.54 9.i0 1.00  68.63 9.33 I.00  68.71 9.23 1.00  68.79 9.64 1.00  68.88 9.85 1.00  68.96 9.94 1.00  APPENDIX 3 Sample computer output of least squares f l of monthly means of DMSL to the function Z M  a+ 0  a,M  f o r ALERT BAY, B.C.  + A cos [2l?/T(M -  M )] 0  5,  <  ?  STAT I C N  173 ALERT •v ~.  NC  INTERMEDIATE 9.5CCC ^<=.5i .t 9.5C94 9.5C94 9.5C9 4 9.5CS4 9.5C94. 9 . 5094• 9.5094  b AY  B r ' ,  >\ s  "/v:y *• . •,.-»*-.•. * \  -A ^  y  E S T I M A T E S C F P A P A ^ E ' T E P S , SLA< 0.0 ' " C . 3 5COC -C.15622E-C2 C.25277 -C. 15575E-C2 C.35395 C.2 5295 .-C.15586E-C2 C. 35395 -C. 1*- £6E-C?,,. C . 25 2 9 5 *c - C . 15 5'8 6 E - C 2 - v . - ; r O , . I 5 5 8 6 E - 0 2 - • 0 . 3 5 39 5 ».>G41556.6E-02 C35395 • • . • - 0 : * : X 5 5 ' 8 4 E - C 2 '.' C.35295 0 .35 39 5 9.5C^4 ;::'U':.' ^'0Vl5'5l 6' E-O2,-.  CF  SCLARES  ..  0. 12746 c. 1 2 8 C 1 0. 12798 c. 12798 0. 12799 0. 12799 c. 12801 c. 12602  c  ;  i  •  l  :  :  :  ;  •KT?.}  •riryf^);^  :  0.9978 2  -  NC C F ITERATIONS M„= 0 . 12 8 0 0  ESFI-KATES->::e'F:;-;^;ARAME;TERS • " ,-  FINAL  CF  1 -  ''>,»-~0..a:55 8 5 £ - 0 2 - -A = 0 . 3 5 3 9 5  9. 5094  SUM  0.. 1 2 9 4 9  f .99779 - C 9 7 84 C .99783 0 .99783 ' G. 99783]. .•<: ,,0.9 9 7 8 3 -v^i0i99783 -  ,  R  c. c  ' * l.cccb"'  c  ;  r  0.99783  12.714  S CU AR ES  '»{*!-, 4 C  tf- ' E S T I M A T E S OF C. 14485  S T A N D A R D (E'£R0i-,:J0 0 . 2%f^$^0*2  MEAN  SEA L E V E L 9.27 ;9.20 9.26 9.34 ;'.>' 9 . 2 9 . • ' 9.4 8 • • 9.75 9.10 9.61 9 .68  T I ME(MjDNTH) 48.46 ' 4 6.54 4 8.63 48.71 46.79 48.86 48 .96 49.04 49 . 13 49.21  ; ;  • • •  • • • • • • • • • • • •  .-.  • • • • • • • •  68.29 68.38 68.46 J 6.8.54 •'*68 .'63  • '  x  68.71  X-**./..  •  :4.8 . 7 9 . •' • 6 8 . 8 8 • 6 8.96'-;  •  6.95 9.13 9.CC " 9 . IC 9 .33 . 9 . 2 2 .... ^ '•9.64- • • 9.85 ,9.^4  THE  PARAMET G . 2 0 577.E  T I T TED MSLX,  WE IGHT l.CC  ,9.. l€7, ' 9 .082 9.i57 9.299  E ;^  :  r.oo;  0. 92705E-O1  0 .1570:5 E - 0 2 = SE(T). '  '.  • . l . C C . :• 1.0 0 ' 1.00  9.•473  ..ll.OC ?>V.OC 1.00 l.OC l.OC  .  • .4  -jv;.-- ..•  9.c56 9.761 9.785 9 . 70 7 9.565  • • • • • •  1  .  ;-;:fy|r ;• ® "  .  •* • • •  «  • • • • • • •  • • • • • •  l.OC I .00  ,  ,:  .i.co  l.OC • •" .'. i . O Q ; v ; , ^.;• :.1 •. ,-'ifcoc . ••.'"'i:.o0i'-; ; *>-51.d0.r/  9.272 9.116 9 .051 9.C74 9.196T9  43b  i  •  ,.v:;;J,.,.: •  9 . 5 3 6 • •'-•-« 9.691'. 9.754.  "  •  -  WEIGHJT%0 "  :  MEAN  - * YJ*  9 . 4 1 6 2 -''.Str = 2.47. .6o -' '-' " ;  :  >:  .":*'' '.i'..;\.v»';" r.V" f  14.494 12.715 12.714 12.714 12.715 12.714 12i7l4 12.715 12.715 12.714 10  APPENDIX  4  Sample p l o t o f monthly means o f DMSL f o r ALERT BAY, B.C. and f u n c t i o n f i t t e d  t o them  APPENDIX 5 L i s t i n g of annual means of DMSL  *****  STATICN  NC 168 VICTCPIA  - 48 -  E C *****  ANNUAL MEANS OF DMSL YEAR  OMSK FT )  WEIGHT  19 9 1910 1911 1912 19 13 1914 1915 1916 1917 1918 1919 19 20 1921 1922 1923 19 24 1925 1926 1927 192 8 1929 1930 1931 1932 1933 19 34 1935 19 2 6 1937 1938 1939 19 40 1941 194 2 1943 1944 1945 1946 194 7 1948 1949 19 50 19 51 19 52 19 53 1954 19 55 1956 19 5 7 19 58 19 59  5.976 6. G26 6 .080 6.G7C 6.C4 5 6.299 6.23 8 6.002 5 .915 6 .194 6.G6 8 6 .050  0 . 87 1. CC 1.00  6.101  1.00  5*987 6 .081 6.021. 6.16 5 6.122 6.179 6. 120 5.919 6.159 6. 19 5 6.178 5.981 6.012 6.029 5.897 6.014 5 .941 5.947 6. 215 6 .369 6.C9 8 6. C58 5.978 6.C47 6.C92 6 .072 6.172 6.€21 6 .153 6.183 6.14 2 6 .189 6.24 3 6.G12 6 .081 6.190 6. 37S 6 .13 8  l.CC 1.00  1.00  1.00 1.00 1.00  l.CO 1.00 1.00  1.00 1.00  .  1.00  l.GG 1.00 1.00  l.CC l.GG 1 .00 1. CO 1.00 0  .58  C. 5 8 1.00 0 .99 l.OG  l.CO  1.00  l.CC 1.00 1.00  l.CO 1.00 1.00  = -;  l.OG  1 .00 1.00 l.GG 0.9 3 1.00  l.CO 1.00 1.00  l.CC 1.00 1.00 l.GG 1.00  i  1  19 60 1961 196 2 IS 63 ' 19 64 1965 19 66 1967 1968  6.C9 1 6. 159 6 .064 6.226 6.G59 ' 6.20 5 6. 189 6.206 6.295  --  l.CC:,:.-' : • : " liOC '•' > i.eo l.CO 1.00 •1 .00 . l.GG'.. l.CC'  ^ ^ f f"'*"^-y-'... 'V, l J  -  4 * 4 * *  STATION NO  169 FULFORD FBR  8 C *****  ANNUAL MEANS CF DMSL YEAR 19 53 19 5 4 19 55 1956 19 57 19 5 8 1959 1960 1961 19 62 1963 1964 196 5 1966 19 67 19 6 8  DMSL(FT) 7 .391 7.451 7. 229 7.294 7.416 7.618 7.420 7.373 7.427 7.295 7.510 7.281 7.417 7.434 7.440 7 .532  WEIGHT 1.00  1.00 l.CC C .86 0 .99 l.GG 1.00  1 .00 1.00 l.OG 0.92 l.OG 1.00 1 .00 l.OG G.9 5  49  -  - 50 *****  STA T I CN ANNUAL  YEAR 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 192 3 1940 19 41 194 3 1944 194 5 1946 1947 1948 1949 1950 19 51 1952 1953 19 54 1955 1956 19 57 1958 1959 1960 1961 1962 1963 1964 1965 1966 19 67 1968  NO  170  MEANS  VANCCUVER OF  B  C  *****  CNSL  DMSL(FT )  WEIGHT  9.92 1 9.98 6 10 .03 2 10. C 7 6 10 -194 10.157 9.922 9.856 10.15 7 10.G62 10.02 1 10 .096 9.97C 10.025 10.106 10.22C 9.646 9.79 7 9. 881 9.912 9 .897 10.CC9 9-862 10.054 10.04 6 9.982 10 .027  C.9C 1.00 1 .00 l.OG l.OG 1 .00 0.43 0.9S 1 .00 l.OG ' l.CC 1.00 l.CC 1.00 0.97 l.GG  10.CSC  9.84 2 9.937 10.0 22 10.200 9 .990 9. 964 10.0 3 6 9.941 10.09 7 9 .9 6 7 10 .061 IC.14C 10.059 10.167  l.CC  1.00 l.CC 1.00 1 .00 l.CO l.OG 1 .00 l.GG 0.98 1 .00 l.OG l.CO 1 .00 l.CC l.CC 1 .00 1.00 1.00 1.00 C.S 6 1.00 1 .00 0.81  l.OG 1 .00  -  - 51 *****  STATION ANNUAL  NO 1 7 1 MEANS  PC I N T OF  ATKINSCN  CMSL  YEAR  D M S L i FT )  WE I G H T  1914 1915 1916 1917 1916 1919 19 2 1 1922 1927 1932 1933 1944 1945 19 4 7 1948 1949 I S 5C 1951 19 5 2 1953 1954 19 5 5 19 56 1957 1958 1959 1960 1961 19 6 2 1963 1964 19 6 5 1966 19 67 1968  10.138 10.C82 9 .904 9 .857 10.127 9 .905 9.984 9.67 8 9 .843 10-081 9.947 9 .798 9.977 9,89 8 10.050 9.938 10.156 10 . 1 5 2 10.097 10.123 10 . 2 1 5 9.977 10.036 10 . 1 6 9 10.24 5 10.097 10 . 0 4 7 10.154 1 0 . 100 10 . 1 9 1 10.047 10. 1 2 6 10.151 10.159 10.258  0.67  1.00 1.00  1.00 l.CC 1.00 1.00 0.37  1.00 0 . 08 1. CC 1.00 1.00 1.00 1.00 1.00 1.00 l.GG 1.00 1.00 1.00 1.00 1 * 0.0 1.00 0.57 0. 9 0  1.00 1.00 C.96 1.00 1.00 l.OC 1.00 1.00  1.00  B C  *****  ***** STATICN  NO 172 TOFINO B C * * * * *  ANNUAL MEANS OF CP SI YEAR  OPSLCFT)  1910  7.352 7.217 7.242 7 .307 7-53 6 7.4 28 7.194 7.296 7.247 7 .124 6.917 7 .269 7 .373 6.990 6 .939 6 .9 21 6.969 7.052 7.110 6 .90 5 7.C 57 7.027 7.G19 7.024 7 .136 6.819 6.926 7 .080 7.218 6.9 26 6.995 7.042 6.926 7 .095 6.829 7.022 7".02 2 7.003 7.136  1911  1912 1913  1914 1915 1916 1917 1918 1919 1920 19 40 1941 1943 1944 1945 1946 1947 1948 1949 19 50 1951 19 52 19 53 1954 19 5 5 19 56 1957 19 58 19 59 1960 19 61 1962 1963 1964 19 6 5 1966 19 67 1968  WEIGHT  l.OO 1.00 l.GG  1.00 1.00 1.00 0.75 0 . 17 1 . CC 1.00 0.88 l.OC 1 .CO  1.00 l.CC 1.00  0.92 0.86 1.00 1.00 1.00 1.00  1.00  C.7 6  l.OC 1.00 I.CO 1.00 1.00  l.OC 1.00  1.00  l.CC  1.00 1.00  l.OC l.OC 1.00  l.CC  - 52 -  4*4*4  STAT ICN  NO  ANNUAL  YEAR  _  1967 1968  MEANS  ALERT OF  9.369 9.341 9.466 9 .39 7 9.433 9.510 9 .554 9.280 9.334 9 .43 2 9.618 9.279 9 .390 9.423 9.372 9 .547 9 . 2 86 9.378 9 .380 9.376 9.46 2  BAY  B  C  * * * * *  DNSL  DMSL(FT)  1948 1949 19 5 0 1951 1952 19 53 1954 1955 1956 1957 1958 1959 I960 1961 1962 1963 1964 19 6 5 .._  173  WEIGHT 0 . 58 1.00 1 . CC 1.00 l.GG 1.00 1.00 1.00 1.00  1.00 1.00 l.CC  1.00 1.00 1 . OC l.CO 1.00  1.00  l.CO 1.00 1.00  - 53 -  *****  STATICN ANNUAL  NC  175 P R I N C E  MEANS  OF  FU PERT  E C  DMSL  VE AR  DMSL(FT )  HEIGHT  19 9 1910 1911 1912 19 12 1914 1915 1916 1917 1918 19 19 19 21 19 2 2 1924 19 27 1939 19 40 1941 1943 1944 1945 19 46 1947 1948 1949 19 50 19 51 19 5 2 1953 19 54 19 55 1956 1957 1958 19 59 1960 1961 1962 1963 1964 1965 1966 1967 1968  12.45C 12.484 12 .407 12.432 12.666 12.814 12 .63 8 12.295 12.385 12.503 12.8C8 12 .413 12.415 12.352 12 .426 12.520 12.657 12.70 6 12.44 7 12.452 12 .424 12.44 6 12.399 12 .498 12.415 12.45 1 12.33 3 12.57 5 12.7 27 12.714 12 .456 12.473 12 .544 12.713 12.617 12.642 12.63 2 12.478 12.733 12.564 12.490 12 .640 12.564 12.786  0.92 C.61 0.5 2 0 . 92 1. CO 1.00 1 .00 l.OC 1.00 1 .00 0.25 0.83 Q.17 l.CG 1.00 1 .00 l.CC 1.00 1 .00 1.00 1.00 1 .00 1.00 1.00 1 .00 1. c c 0.92 1 .00 l.OC 1.00 1.00 1.00 1.00 1 .00 0.9 7 0.95 1.00 1. GG 1.00 1 .00 1.00 1.00 1 .00 1.00  *****  54 -  APPENDIX 6 P l o t s of annual means of DMSL f o r VICTORIA,B.C. and  FULFORD HARBOUR, B.C. and l i n e a r regression l i n e s  -  APPENDIX 7 P l o t of annual means of DMSL f o r VICTORIA, B.C. and quadratic regression  line  57 -  APPENDIX 8 P l o t s of annual means of DMSL f o r VANCOUVER, B.C. and POINT ATKINSON, B.C. and l i n e a r regression l i n e s  - 61 -  APPENDIX 9 Plot of annual means of DMSL f o r TOFINO, B.C. and  l i n e a r regression l i n e  - 63 -  APPENDIX 10 P l o t of annual means of DMSL f o r ALERT BAY,B.C. and  l i n e a r regression l i n e  - 65 -  APPENDIX 11  P l o t of annual means of DMSL for PRINCE RUPERT, B.C. and  l i n e a r regression l i n e  -  APPENDIX 12 Sample computer o u t p u t o f l e a s t squares f i t o f a n n u a l means o f DMSL t o t h e f u n c t i o n Z>_- a + a,Y 0  w i t h t e s t o f s i g n i f i c a n c e f o r a, f o r ALERT BAY, B.C.  V  67  -  #«*** STATION NO 173 ALERT BAY B C  v "• r  -  68  -  • J: ';*:,• :' . • I.N T E FM EC I AT E EST IM AT ES CF PAPAMETEFS, SUM OF •SQUARES 1861 .9 co.v' o.o :  ;  FINAL ESTIMATES OF PARAMETERS 9.4727 -0.97179E-03 SUM CF SQUARES  -.: i  0.14954  ESTIMATES CF STANDARD ERROR OF TF E PARAMETER C. 19159 0.32747E-02 FRATIC FOR PARAMETER FPROB FOR PARAMETER TIME,YEARS) 48.G 49.0 50.C 51.C 52.0 5 3.0 54.0 55.0 56.0 57.0 58.0  59.0 60.C 61.C 62.C 63.0 64.0 65 .0 66.0 6 7.0 68.0  2 = 2 =  t  VI"  • '  i *  0.C881 C.7623  MEAN SEA LEVEL 9.369 9.341 9.466 9.39 7 9.433 9.510 .9.5 54 9.280' 9.324 9.4 2 2 9.618 9.379 9.390 9.423 9.27 2 9.547 9.286 9.378 9.3 80 9.37 6 9.463  WEIGHED MEAN = 9.4 166  i  $  WEIGHT 0.5 8 1 .00 1.00 l.CC 1.00 1 .00 1 .OC 1 .00 1 .CO 1 .00 1 .00 1.00  1.00 1 .00 1.00  1.00 1 .00 1.-00  1 .00 1 .00 1 .OC "  SUM. = 2C.5 8 ;  FITTED MSL 9.4260 9. 425C 9.4241 9 . 4 231 9.4221 9.4212 9.4202' 9.419 2 9.4182 9.4173 9.4163 . '. 9.4153 9.4143 9.4134 9.4124 9.4114 9,4105 9.4095 9.4085 ' • 9*4075 • . •9.40 66: jgi. . •  •  '-.  

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