Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1971_A7 S54.pdf [ 9.53MB ]
Metadata
JSON: 831-1.0050565.json
JSON-LD: 831-1.0050565-ld.json
RDF/XML (Pretty): 831-1.0050565-rdf.xml
RDF/JSON: 831-1.0050565-rdf.json
Turtle: 831-1.0050565-turtle.txt
N-Triples: 831-1.0050565-rdf-ntriples.txt
Original Record: 831-1.0050565-source.json
Full Text
831-1.0050565-fulltext.txt
Citation
831-1.0050565.ris

Full Text

SEASONAL AND SECULAR VARIATIONS OF SEA LEVEL WITH SPECIAL REFERENCE  TO THE CANADIAN PACIFIC COAST by HAJO F.W. SIEBENHUENER Dipl.-Ing., Technische Universitaet Berlin, 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 this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1970 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r ee t h a t t he L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f C i v i l Engineering The U n i v e r s i t y o f B r i t i s h Co l umb i a Vancouve r 8, Canada Date March 22, 1971 - i i -ABSTRACT In the f i r s t part of this thesis definitions of sea level are given and causes and effects of i t s seasonal and secular variations are brie f l y discussed. The second part deals with the numerical determination of these changes on the coast of British Columbia. Using raw tida l data in the form of monthly means of sea level, seasonal variations are determined as annual oscillations with mean amplitudes between 5 and 12 cm for seven stations on the B.C* coast. The investigation of secular variations i s based on (raw) annual means of sea level. These variations are essentially represented by linear trends which are s t a t i s t i c a l l y significant at the stations VICTORIA, VANCOUVER, POINT ATKINSON and PRINCE RUPERT, where they indicate submergence. Assuming an eustatic r i s e of sea level at the rate of 1.0 mm/yr, the influence of land movement on submergence is estimated. For VICTORIA, a probable land u p l i f t since 1909 and for VANCOUVER, POINT ATKINSON and PRINCE RUPERT a definite land subsidence since about 1943 i s found. The rates of land subsidence range between 1 and 2 mm/yr. - i i i 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 variations 3 2.1.2. Quasi-periodic variations 6 2.2. Factors Influencing Physical Mean Sea Level (PMSL) 8 2.2.1. Movements of the earth's crust 8 2.2.2. Movements of sea level 10 2.3. Factors influencing Derived Mean Sea Level (PMSL) 12 2.4. Comprehensive consideration of factors influencing sea level 15 3. SEA LEVEL ON THE CANADIAN PACIFIC COAST 18 3.1. Presentation and discussion of data 19 3.2. Analysis of PMSL 22 3.2.1. Seasonal variations of DMSL 22 3.2.2. Secular variations of DMSL 24 3.3. Discussion of results 28 CONCLUSION 32 BIBLIOGRAPHY 35 APPENDICES . 37 - i v -LIST OF TABLES Page Table I. The long period harmonic t i d a l constituents (after Doodson) 4 Table II, Summary of factors influencing DMSL 16 Table III. Gauge station index 19 Table IV. Time-spans of available t i d a l records 22 Table V, Amplitude, period and phase lag of seasonal o s c i l l a t i o n 24 Table VI. Table of regression coefficients 28 Table VII. Rates of PMSL, relative and land movement 31 - V -LIST OF FIGURES Page Figure 1, Components of sea level variation at Esbjerg (Denmark) 18 Figure 2, Map of gauge locations on the Canadian Pacific coast 20 - v l -LIST OF APPENDICES Page Appendix 1. Sample l i s t i n g of d a l l y means of DMSL f o r ALERT BAY, B.C. (1967) 37^ Appendix 2. Sample l i s t i n g of monthly means of DMSL f o r ALERT BAY, B.C. (1948 - 1968) 39 Appendix 3. Sample computer output of least squares f i t of monthly means of DMSL to the function ZM - a D + a LM + A cos [ziT/TCM - MQ)] fo r ALERT BAY, B.C. 43 Appendix 4. Sample p l o t of monthly means of DMSL f o r ALERT BAY, B.C. and function f i t t e d to them 45 Appendix 5. L i s t i n g of annual means of DMSL 47 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 55 Appendix 7. Pl o t of annual means of DMSL f o r VICTORIA, B.C. and quadratic regression l i n e 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 59 Appendix 9. Pl o t of annual means of DMSL f o r TOFINO, B.C. and l i n e a r regression l i n e 61 Appendix 10, Pl 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 63 Appendix 11. Plot of annual means of DMSL for PRINCE RUPERT, B.C. and l i n e a r regression l i n e 65 Appendix 12. Sample computer output of le a s t squares f i t of annual means of DMSL to the function Z y- a 0+ 3 l Y with test of s i g n i f i c a n c e of for ALERT BAY, B.C. 67 - v i i -ACKNOWLEDGEMENTS Thanks are due to Mr. G. Dohler and Mr. S.O. Widen, both of the Canadian Hydrographic S e r v i c e , f o r supptylng the t i d a l data 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 the advice given me by Dr. S.H. de Jong, 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 of the Department of C i v i l Engineering of the U n i v e r s i t y of B r i t i s h Columbia. In p a r t i c u l a r I wish to thank P r o f . H.R. B e l l f o r c a r e f u l l y checking the manuscript f o r c o r r e c t E n g l i s h . Vancouver November, 1970 H. Siebenhuener - 1 . INTRODUCTION The study of sea level, the causes and effects of i t s changes, and attempts to separate vertical movements of the sea from similar movements of land is an aspect of geophysics which has only received world-wide attention in comparatively recent years. Of even more recent origin i s the realization by geodesists and hydrographers - to mention only two kinds of specialists - that each has a common interest in the subject. As recently as fifteen years ago, hydrographers tended to have an exaggerated idea of the accuracy of national levelling nets, while geodesists tended to have similar misconceptions of the s t a b i l i t y of sea level. It i s one thing to record facts but quite another to interpret them, and the study of sea level i s no exception to this general proposition. We wish not only to observe and record what has happened and what is happening, but also to account for what i s observed, in order, i f possible, to look ahead and forecast l i k e l y trends. Once one starts to look for causes of changes in sea level, 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 glaciers, of climatic changes, of crustal movements of the earth and many other factors. In fact the study of sea level interlocks with many other - perhaps nearly a l l - geophysical problems* In view of the above, this study i s subdivided into three main sections. In preparing the thesis the necessity for and the lack of clear-cut definitions became obvious; they are given in section 1. In section 2 some of the under-lying concepts are summarized. The intention is to convey some idea of the complexity and variety of factors influencing sea level. In section 3 the results of the numerical work are given. This section consists essentially - 2 -of a s t a t i s t i c a l analysis of available t i d a l data on the coast of British Columbia and an interpretation of the results. No attempt is made to correct raw t i d a l data for disturbing meteorological influences such as a i r pressure, temperature and prevailing winds. 1. DEFINITIONS OF SEA LEVEL The investigation in the following sections makes frequent use of three terms which are defined as follows: i) "Physical Sea Level" (PSL) at any place is the physical boundary between ocean and a i r . i i ) "Physical Mean Sea Level" (PMSL) at any place is the average of the continuously changing height of Physical Sea Level with respect to land over a l l stages and periods of a l l astronomical tides. i i i ) "Derived Mean Sea Level" (DMSL) at any place is the average of measured values of Physical Sea Level over a certain period and is referenced to a bench mark and hence a datum. The common feature of the three kinds of sea level as defined above i s their time and space dependence; the latter i s not dealt with in this thesis since i t can only be studied on a world-wide basis. Definition i) is self-explanatory. PSL and PMSL di f f e r in that PSL is affected by the tides whereas PMSL is not affected by the tides. The difference between PMSL and DMSL is a conceptual one and rests on the fact that PMSL exists regardless of the existence of man and his action while DMSL comes into being only when man builds a tide gauge station, more or less continuously measures sea levels and analyzes them. - 3 -Two examples i l l u s t r a t e the concept behind this distinction: 1) It makes complete sense to say: "The annual value of DMSL in 1948 for station No. 173 is 9.37 feet above datum." Replacing DMSL by PMSL yields nonsense because PMSL cannot be measured and hence cannot be represented by a number. 2) While i t is in order to say: "PMSL is subject to secular variations due to g l a c i a l action", replacement of PMSL by DMSL does not make sense because a DMSL value as such is not affected by physical action. PMSL i s best thought of as a geophysical phenomenon whereas DMSL is best regarded as a number which describes this phenomenon more or less accurately. This distinction proves to be useful in the discussion of the various factors influencing sea level. 2. FACTORS INFLUENCING SEA LEVEL Because of the limited scope of this study the discussion of factors influencing sea level must be restricted to a brief description of the effect of each factor. Where available, a numerical estimate of the effect on sea level i s given. In order to f a c i l i t a t e reference to factors, 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 variations 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 variations (1) The Tides. The tides are caused by the variable attraction of the moon and the sun and consist of many harmonic constituents, the periods of - 4 -which range from several hours up to approximately nineteen years. Daily, monthly and yearly values of DMSL are normally derived from observed data by methods specifically designed to eliminate, as e f f i c i e n t l y as possible, t i d a l oscillations having periods up to and including a lunar day. A daily mean, for example, is generally computed from observations at intervals of an hour by simple averaging, by application of numerical f i l t e r s , or by integration of graphical records. The figures 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 lis t e d in Table I, taken from Doodson's harmonic development of the tide generating potential (Doodson, 1921). They are relevant when one considers seasonal and secular variations. Table I. The long period harmonic t i d a l constituents (after Doodson) Angular speed Name Symbol in degrees Period Equilibrium^ per mean solar in days amplitude hour in cm Lunar fortnightly Mf 1.0980 13.7 2.10 Luni-solar fortnightly Msf 1.0159 14.8 0.18 Lunar monthly Mm 0.5444 27.6 1.11 Solar semi-annual Ssa 0.0821 182.6 0.98 Solar annual Sa 0.0411 365.2 0.15 Nodal - - 0.0022 18.62yrs - 0.88 The amplitudes are associated with the latitude coefficient (1 - 3cos S), where Q is co-latitude. The amplitudes are those appropriate to the equilibrium tide, the tide that would be experienced in an ocean which completely covers the earth and responds instantaneously to the tide generating forces of the sun and the moon. In nature the presence of irregular coastlines and variations in bottom topography prevent the equilibrium tides from being realized in amplitude and phase, unless their period is so long that equilibrium may be assumed to exist. The lunar fortnightly and monthly tides Mf and Mm are generally very small in size and have not evoked much interest. The small luni-solar tide 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 variations in shallow depths; thus in coastal areas and estuaries Msf i s generally quite unrelated in amplitude and phase to i t s equilibrium form. Monthly values of DMSL w i l l obviously contain negligibly small contributions from Mf, Msf and Mm. Their most striking feature i s the seasonal variation, which i s customarily represented by the solar annual and semi-annual tides, Sa and Ssa, though in fact by far the greater part of these oscillations i s not of t i d a l origin but of meteorological or oceanographic origin (See factors (2),(3) below). The latest attempt to estimate the t i d a l contributions to seasonal variations was under-taken by L.F. Ku, who applied power spectra analysis to monthly means of DMSL (Ku, 1970). His values of Sa for the North Atlantic and North Pacific coast are identical and are about 1.2 cm. The nodal tide arises from the precession of the moon's nodes with a period of 18.62 years. It 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 for believing that in nature this tide should have an equilibrium form, suitably corrected for 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 reliable series of DMSL exist for study and in latitude 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 variations from various sources which are always present. Rossiter writes: "The theoretical existence of this tide i s frequently - 6 -used as an argument for taking 19-yearly means, or taking a 19-year span of observations when examining data for variations of many kinds, yet i t s distribution and magnitude cannot be said to have been determined analytically" (Rossiter, 1962). The situation i s similar, and for much the same reasons, in the case of the pole tide. This os c i l l a t i o n which has a period of approximately 14 months was not included in Doodson's l i s t of t i d a l constituents, but may be expected to exist as a result of the in s t a b i l i t y of the earth's instantaneous axis of rotation. It has been shown that the equilibrium form of this tide should have an amplitude of the order of 5 mm (Haubrich and Munk, 1959). Attempts to identify i t in DMSL data appear to have confirmed the existence of an osci l l a t i o n with a period of 14 months, though in general the amplitudes are more than twice the expected value. In contrast to these s t r i c t l y periodic variations which are due to gravitational forces and the periods of which can be derived analytically from the equilibrium theory of tides, quasi-periodic variations are due to factors restricted to the earth or parts of i t . 2.1.2. Quasi-periodic variations Quasi-periodic changes in PSL are those of seasonal nature. Monthly means of DMSL at any station show a more or less consistent pattern year by year, and these have been intensively studied on both a local and a global scale ( L i s i t z i n and Pattullo, 1961; Pattullo, 1963). There are at least three factors involved which may be cl a s s i f i e d as "meteorological", "oceanographic" and "fresh water flow". (2) Meteorological effects. Meteorological effects account for a considerable - 7 -part of the seasonal variation in latitudes above 45°. They are the response of PSL to seasonal changes in atmospheric pressure and pre-valling winds. If the time rate of change is slow, as discussed here, PSL acts almost instantaneously as an inverted water barometer; theoretically i t should rise 1 cm per 1 mb f a l l in a i r pressure and vice versa. In a l l latitudes seasonal movements and variations in intensity of high and low pressure systems result in sea level changes which may amount to 8 cm in amplitude. Wind fie l d s may be defined in terms of air pressure distributions 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 result 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 effects. These effects, combined with meteorological components, account for seasonal variations of PSL in lower latitudes. Regardless of how they are generated, great ocean currents such as the Gulf Stream create surface gradients with seasonal variations. Of more direct oceanographic origin are steric changes in PSL. A steric phenomenon i s one which involves the molecular dimensions of the material in question. In sea water, steric effects are brought about by temperature changes and by variations in s a l i n i t y (and thus density). Observations of the time-dependent structure of density with depth in the oceans have been used to compute seasonal changes in steric level; i t has been shown that over large areas these variations can account for a large proportion of observed changes in PSL. For instance, a seasonal rise and f a l l of shelf and estuary water temperatures may O exceed something of the order of 10 C over a 10 m depth range; the - 8 -calculated effect would be 15.5 mm steric rise and f a l l . (4) Fresh water flow. Fresh water flow is the third major cause for quasi-periodic changes in PSL. Whether due to monsoon rains or melting snow, the flow i s essentially seasonal, almost to the extent of being predictable. In the v i c i n i t y of a river mouth this effect may amount to 10 cm. In concluding this section on factors influencing PSL i t may be mentioned that the usual amplitude of "annual tides", as seasonal variations are some-times called, i s 10 to 15 cm (Pattullo, 1963). 2.2. Factors influencing Physical Mean Sea Level (PMSL) According to the definition of PMSL, one may imagine PMSL as a PSL which is free of the effect of the astronomical tides. Since i t i s possible to free PSL of astronomical tides only i f a span of about 19 years is considered, obviously the influence of "annual tides" i s also eliminated. However, the elimination of astronomical and annual tides does not stabilize PMSL. Since slow but continuing changes in PMSL are a common feature at most stations, i t i s customary to refer to them as secular changes, and to consider them in terms of steady changes in annual DMSL. For simplicity and since their definition from observed data i s not usually precise, a linear change i s assumed, although there is no physical reason to j u s t i f y a linear law. In fact, i t has been considered in some instances that quadratic or even cubic mathematical expressions describe secular variations more precisely. Since PMSL i s considered with respect to land, the factors influencing i t can be subdivided into vertical movements of the earth's crust and movements of sea level (Valentin, 1952). 2.2.1. Movements of the earth's crust (5) Tectonic movements. Deformations of the crust of the earth in geological - 9 -eras are referred to as tectonic movements. They are caused by isostatic adjustment, orogenesis (mountain building) and/or sedimentation. (5a) Tectonic movements due to isostatic adjustment. These movements are encountered in 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 regionally loaded while the pressure of water masses on the ocean floors decreases everywhere. In order to restore equilibrium, loaded continental regions must sink and a l l ocean floors in the world must r i s e . When icecaps melt during a "warm" period, the opposite process takes place and PMSL rises again. Continental regions are then relieved and tend to rise to their original level again, while the ocean floors are depressed by the increased water load. Today, maximum rates of isostatic u p l i f t of land of nearly 40 mm/yr after deglaciation have been measured in south-east 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 crust, takes place in so-called orogenic belts which are regions having zones of strongly negative gravity anomalies (subsidence) and strongly positive gravity anomalies ( u p l i f t ) . The latter today generally correspond to the folded mountainous belts. This phenomenon i s indicative of an incomplete isostatic compensation. The rates of u p l i f t or subsidence vary considerably according to the intensity of seismic activity in the region considered. (5c) Tectonic movements due to sedimentation. Sedimentary basins are, geo-logi c a l l y speaking, c l a s s i f i e d as "contemporary geosynclines" of various classes. As a rule, they are identified geomorphologically by their long,, low, sandy coasts. Although their outlines are straight and the - 10 -hinterland may display wide areas of recently emerged coastal plains, these coasts are often coasts of submergence''. From deep bores, i t is apparent that these basins have been discontinuously in subsidence for 6 9 periods of the order of 10 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, regionally limited processes affect PMSL. Sag due either to sedimentary compaction or to sedimentary collapse causes local subsidence of the coast and leads to an apparent rise of PMSL. To i l l u s t r a t e , great man-made works, coastal engineering works, harbours and harbour jetties in the v i c i n i t y of a gauge station can simulate trends in PMSL, the rate of which i s hard to assess. 2.2.2. Movements of sea level 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 referred to as eustatic changes and are mainly due to glacial action. (7) Glacio-eustasy. Glacio-eustasy is caused by the world-wide effect of a hydrological imbalance between world moisture transport to the continents (snow) and, in reverse, to the oceans (meltwater). The imbalance of these processes in gla c i a l periods of the earth's history has especially affected the volume of ocean water and the position of PMSL. In each ice age, part of the hydrosphere was bound to extensive inland icecaps thus making sea level 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 glaciation and multiply i t by the mean thickness of ice, thus obtaining the volume of ice. A knowledge of the volume of ocean water may then be used to estimate the change in PMSL; second, one may try to locate the geomorpho-logical and geological marks of old 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 radio-carbon dating. Using the f i r s t method and allowing for isostatic u p l i f t of the relieved ocean floors, Fairbridge estimates that during the last ice age PMSL was about 100 m below present PMSL. A complete melting of a l l existing glaciers would result in an eustatic rise of PMSL of about 35 m (Fairbridge, 1961b). Applying the second method, Mathews ascertained that at the shore of southwestern British Columbia an eustatic rise of PMSL at a mean rate of 1.2 mm/yr has taken place for the last 8000 years (Mathews et a l . , 1970). This figure agrees with the results of a pioneer study by Gutenberg using data from world wide tide gauge records and suggesting an eustatic rise of PMSL at 1.1 mm/yr during the f i r s t half of this century (Guten-berg, 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 in section 3. (8) Other eustatic changes. Apart from glacio-eustasy, two other significant factors in world-wide change of PMSL are recognized; sedimento-eustasy, due to accumulation of sediments in ocean basins, thus causing a one-way, positive s h i f t ; and tectono-eustasy, due to modification in the shape of ocean basins because of tectonic action, thus being either positive or negative in effect. Both of these changes are related to the dimensions of the container while glacio-eustasy relates to the volume of the contents. It has been estimated that the sedimento-eustatic rise ln PMSL - 12 -amounts to 0.01 to 0.02 mm/yr. Even i f the effects of tectono-eustasy and sedimento-eustasy should happen to be of the same sign during a certain stage of the earth's history, 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 history. Summarizing, i t can be said that tectonic and eustatic movements are the main components influencing PMSL. It is obvious that they also affect PSL. 2.3. Factors influencing Derived Mean Sea Level (DMSL) Changes in PMSL can only be considered theoretically and qualitatively; quantitative statements about the rates of change are only possible via DMSL. One has to establish a tide gauge station, 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 position of PMSL. This discrepancy is due to the fact that DMSL i s affected by various factors which have nothing to do with PMSL but relate only to the gauge and i t s handling. In general these factors have the character of errors, and the more effectively they are eliminated, the more closely w i l l DMSL coincide with PMSL. (9) Errors of reading the level on the tide pole. To check automatic tide gauges i t i s necessary to read sea level on the corresponding tide pole (situated in the immediate vicinity) at least once a day. Since these readings are used to correct measurements obtained from automatic gauges, their reading errors influence those measurements. Random reading errors arise from sea waves, the quality of the markers, the length of the line of sight to the pole, lighting conditions (position of the sun), and the pecularities of the observer. If measurements are taken once a day, the resulting standard deviation in an annual value of DMSL - 13 -Is approximately + 1 mm. The systematic errors resulting from errors in the scale of the pole and from errors resulting from connecting individual 1 meter (or foot) sections of the pole are of the same order of magnitude (+ 1 mm). (10) Errors in the behaviour of the tide gauge. Instrumental errors of a tide gauge can result in changes in the recording scale, in the rate of feed of the recording tape, in the distance between the time markers, and in the height or additive constant of the tide gauge. Small changes in the recording scale do not influence the accuracy of determination of DMSL, since maximum and minimum values are affected alike. Changes in the recording tape feed can result in an error i f printed tape is used, although this error is negligible. Changes in height of the tide gauge or in the additive constant have a direct bearing on DMSL. How-ever, they are eliminated by comparing the recordings with the tide pole observations. (11) Errors made in analysing the ntareograms. Variations in the dimensions of the printed recording tapes prior to measurement and errors in the divisions give rise to differences in the scale of the tide gauge and that of the printed subdivisions. The errors in length of the paper, i f properly stored, are less than 1 : 1000. This additional small error in scale has no bearing on the calculation of DMSL. The standard deviation when evaluating the mareograms can be as large as + 5 mm for a single value on a scale up to 1 : 20. The resulting standard deviation for an annual DMSL value amounts to about + 0.2 mm i f four measurements are taken each day. (12) Levelling errors. In order to f i x and to check the height of the zero point of the scale on the tide pole with reference to the tide gauge datum ( t i d a l or chart datum), the height differences relative to the - 14 -t i d e gauge bench marks situated i n the v i c i n i t y are normally measured annually. In t h i s process, various random and systematic e r r o r s occur and t h e i r influence on the DMSL of any given year i s of a systematic nature. Today, a mean e r r o r i n double l e v e l l i n g of + 0.5 to 1.0 mm/"\/km' can be obtained with c a r e f u l observation, depending on the type of instrument employed and the distance to be covered. R e l a t i v e l y large a d d i t i o n a l e r r o r s are introduced as a r e s u l t of measuring the connection between the scale of the gauge and the t i d e pole because the l a t t e r f r e q u e ntly i s not 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 . In a d d i t i o n , random height e r r o r s of the t i d e gauge bench marks exert the same influence. Thus the standard d e v i a t i o n i n an annual value of DMSL r e s u l t i n g from l e v e l l i n g e r r o r s can be expected to be about + 2 mm. (13) E r r o r s i n height. The main cond i t i o n to be met by a t i d e pole i s that i t s height must remain constant or that p o s s i b l e e r r o r s i n height must be taken into c o n s i d e r a t i o n . I f a change i n height due to atectonic movements ( f a c t o r (6)) i s detected with the a i d of annual l e v e l l i n g checks, i t i s not p o s s i b l e to state anything d e f i n i t e about the temporal course of the change. The standard d e v i a t i o n associated with t h i s c o n d i t i o n f o r an annual value of DMSL i s estimated to about + 1 mm to + 2 mm. The heights of bench marks, sometimes attached to b u i l d i n g s , are not always constant e i t h e r . To sum up, the following e r r o r components normally have a bearing on an annual value of DMSL: - E r r o r s of reading the l e v e l on the t i d e pole • e^ «• + 1.0 mm - Errors i n the t i d e pole scale and i n s t a l l a t i o n &2 " — 01111 - E r r o r s made i n analysing the mareograms e - + 0.2 mm - 15 -- Levelling errors and errors in measuring connection of bench mark to tide pole • e4 ", i 2.0 mm - Variations in the height of the tide pole e^ «•+ 1.5 mm A comparison of individual error components shows that the main sources of errors arise from height checks and height changes of the tide pole. When they are considered over decades, the errors quoted are random and the corresponding total standard deviation associated with annual values of DMSL can be computed from the law of error propagation: ~\ l~2 2 2 2 2 - 1 Total standard deviation ™ \ / e i + e2 + e3 + e4 + e5 « + 3 mm (0.01 f t ) . This figure of + 3 ram (0.01 ft) is also given by Montag (Montag, 1970) while Rossiter states a more optimistic but rather unrealistic estimate of + 1 mm (Rossiter, 1962). 2.4. Comprehensive consideration of factors influencing sea level Once one tri e s to determine changes in sea level numerically one has to deal with DMSL values. Now DMSL i s influenced not only by the factors mentioned in section 2.3., but obviously also by factors (1) to (8), inclusive, these factors being of widely different origin. Table II gives a summary of the factors which tend to produce seasonal and secular changes 2 of DMSL . The observations are only the ultimate resultant of a l l components. In his paper "An Analysis of Annual Sea Level Variations in European Waters" Rossiter tried to separate some components using annual values of DMSL, meteorological and astronomical data (Rossiter, 1967). The investigation was based on a mathematical model of the form 2) There are other factors which affect the basic height ( i . e . an arbitrary working datum) and/or cause stochastic contributions to values of DMSL. The reader interested in those factors is referred,to the references (Wemelsfelder, 1970) and/or (Montag, 1970). Table II. Summary of factors influencing DMSL Movements of the earth's crust Movements of sea level Movements assoc. with the gauge Tectonic Atectonic Eustatic Aneustatic Factor No. (5) (6) (7),(8) (1),(2),(3),(4) (9),(10),(ll),(12),(13) Cause Isostatic adjustm. orogenesis sedimentation Various kinds of sag Glacio-eustasy, sedimento- and tectono-eustasy Tidal movements, meteorological * oceanographic effects,freshwater Operation of tide gauge Effect U p l i f t and/or subsidence of continents and ocean7f loors Localized subsidence of land World-wide rise of DMSL As to time and locally limited r i s e and f a l l of DMSL Height changes of tide pole Character Secular Unpredictable Secular Periodic Errors in observation Detectable by Precise levelling plus tide gauge records Precise levelling Tide gauge recordsv Tide gauge records Careful operation of gauge Appr. rate of change Max. rate of change 40 mm/yr (Alaska) Varies considerably Rise at about 1.0 mm/yr Varies according to period + 3 mm/yr (+ 0.01 ft/yr) (Accuracy of annual DMSL value) I t—» - 17 -Z y - Y P + 5 Z br Br + c i c o s < N ) • c 2sin(N) • <(>Y , where Is an annual value of DMSL, referred to some arbitrary working datum, for the year Y, Y i s the year number relative to 1900, an annual mean value of air pressure, corrected to "mean sea level", at station r , for 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 coefficients a , b , c, and c_ are to be determined by regression P r I 2 computations according to the method of least squares. Thus in the above equation the polynomial ^ ] a p Y P represents a secular variation, providing the choice between a linear (p-1), a quadratic (p~2) and a cubic (p-3) expression. The term ^ j b rB accounts for atmospheric contributions and r = i the terms CjCos(N) and c^sinCN) express the osci l l a t i o n due to the nodal 3 tide . A graphical representation of the various components of Zy i s given in Figure 1 for Esbjerg, Denmark (Courtesy of Royal Astronomical Society, London). For purposes of this study, the most important contribution to the observations i s the secular variation. It i s the resultant of a relative movement between sea level and land and is produced either by shift of the land ( u p l i f t or subsidence) or by eustatic changes in PMSL, or both. A positive secular variation (as shown in Figure 1) i s referred to as coastal submergence while a negative variation i s referred to as emergence. The introduction of these new terms leads to the second part of this thesis. Considering only the coast of British Columbia, seasonal veriations in DMSL and trends of emergence and/or submergence are investigated. 3) Further explanation of the terms is found in (Rossiter, 1967) - 18 -Figure 1. Components of sea l e v e l v a r i a t i o n at Esbjerg, Denmark (Units are mm) 200 100 200 100 100 r--100'--50 >-Esbjerg o IO et T I I Observotlons Secular variation Atmospheric contributions Nodal tide Residuals (Courtesy of Royal Astronomical Society, London) 3. SEA LEVEL ON THE CANADIAN PACIFIC COAST As indicated in the int r o d u c t i o n , t h i s section i s concerned with the numerical determination of seasonal and secular v a r i a t i o n s In sea l e v e l on the coast of B r i t i s h Columbia, based on monthly and annual DMSL values. The presentation and discussion of 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 Pacific coast. Their locations are shown in Figure 2. Seven of these stations have suff i c i e n t l y long records for purposes of this study. The seven stations are lis t e d in Table III together with geographic position, bench mark and datum information of each. Table III. Gauge station index Sta.No. Location Latitude Longitude Bench mark Reference North West No. El . ( f t ) datum 168 Victoria 48°25.47' 123"22.17' 737-J ,15.40 Chart Datum 169 Fulford Harbour 48 45.84' 123 26.90' HS-1-1952 12.16 Chart Datum 170 Vancouver 49 17.35' 123 06.98' Brass Plug 42.15 Chart Datum 171 Point Atkinson 49 20.26' 123 15.15' HS-118-1950 21.33 Chart Datum 172 Tofino 49 09.30' 125 54.50' HS -1-1940 12.93 Chart Datum 173 Alert Bay 50 35.23' 126 56.78' HS-1947 24.59 Chart Datum 175 Prince Rupert 54 18.90' 130 19.70' HS-1944 32.49 Chart Datum At Victoria and Vancouver the primary bench marks as stated in the above table are also used for geodetic purposes while at the other stations bench marks were exclusively established for 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 available by the Canadian Hydrographic Service in form of daily values of DMSL. They are given in feet and decimals of a foot and stored on punched cards which are accompanied by a printed computer output. A sample page of this l i s t i n g is shown in Appendix 1. It shows the daily values of DMSL observed at the gauge station of ALERT BAY in 1967. The following additional information was available for each of the seven stations: - a description of the gauge station together with a chart showing the location 4) Chart Datum is a low water datum which by international agreement i s so low that the tide seldom f a l l s below i t . It is used only in the v i c i n i t y of the gauge location and dif f e r s from place to place, depending on the range of the tide. - 21 -of the gauge and the area within a radius of about 1 mile of the gauge; - the methods by which elevations were originally established and have been maintained during the period of operation; - a chronological table showing the history of bench marks and tid a l datum elevations; - a l i s t and description of bench marks used for reference; and - a tabulation of bench mark elevations. A detailed examination was made of these data. The following points emerged: 1) the sites of the gauging stations have been altered in some instances, thus introducing uncertainties in the order of levelling accuracy; 2) chart or t i d a l datum has been altered at some stations. However, since a datum is established by definition and not by observation, this does not affect values of DMSL; 3) annual levelling checks have not been consistently recorded although they may have been carried out. Where they were, however, the figures show that since about 1940 the height difference between zero point of the tide pole and bench mark remained constant to + 3 mm (0.01 ft) 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 (0.01 f t ) ; 5) although observations have been taken almost continuously at most stations since about 1909, parts of older records no longer exist. This is the reason for the gaps in the time-spans of available records shown in Table I - 22 Table IV. Time-spans of a v a i l a b l e t i d a l records Sta.No. L o c a t i o n Continuous record No. of Annual l e v e l l i n g from - t o years checks recorded 168 V i c t o r i a 1909 1968 60 Since 1941 169 F u l f o r d Harbour 1953 m 1968 16 A l l 170 Vancouver 1910 1923 14 A l l 1943 - 1968 26 A l l 171 P o i n t Atkinson 1914 - 1919 6 A l l 1947 — 1968 22 A l l , except 1952 172 T o f i n o 1910 - 1920 11 A l l , except 1910 1943 1968 26 A l l 173 A l e r t Bay 1948 • 1968 21 A l l , exc. 1950,52 175 P r i n c e Rupert 1909 1919 11 A l l , exc. 1916-19 1943 mt 1968 26 A l l 3.2. A n a l y s i s o f DMSL 3.2.1. Seasonal v a r i a t i o n s of DMSL The i n v e s t i g a t i o n of seasonal v a r i a t i o n s c o n s i s t e d of the f o l l o w i n g three steps: 1) Monthly means o f DMSL and weights 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 s t a t i o n : The conversion of months and years i n t o decimals of a year was achieved by the formula M - Y + ( N M - 0.5)/12 , where M i s the time i n t e r v a l i n years and decimal f r a c t i o n of a year between the year 1900.0 and the mid-point of any month i n any given year t h e r e a f t e r , Y i s the year number r e l a t i v e to 1900.0, and Nj^ i s the number of the month i n the year Y. As an example, June 1948, f o r which Y « 48.0 and N^ - 6, i s represented by the number 48.46. Monthly means were computed by t a k i n g the simpl average of a l l d a i l y means a v a i l a b l e i n the 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 according t o the - 23 -formula WM"V ND' where i s the weight associated with the monthly mean , N. i s the number of daily means available in a given month M, and N Q is the number of days in that month M. The fact that February has 29 days in a leap year was taken into account both in the computation of monthly means and their weights . A sample computer output of the tabulation i s given in Appendix 2 for station No. 173, ALERT BAY, B.C. 2) Employing the technique of least squares f i t , an appropriate regression was performed for each station. For a l l stations the regression function was chosen to be of the form - a Q + aj.M + A cos [zir/TCM - MQ)j , where Z w i s a monthly value of DMSL, referred to Chart Datum, for the month M, a Q represents a mean value of DMSL at 1900.0, a^ represents a linear secular trend, M i s the month in decimals of the year Y, A is 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 MQ is i t s phase lag. No further sinusoidal terms were considered because the purpose was not to carry out a harmonic analysis but rather to determine the amplitude A, the period T and the phase lag MQ of a suspected seasonal o s c i l l a t i o n . The term ajM was included to account for a possible secular trend at least linearly. In view of the above, a 0, a p A, T, and MQ were introduced as co-effi c i e n t s to be determined together with their standard errors (SE) - 24 -according to the method of least squares f i t . Most probable values for the five coefficients and their standard errors were computed with the aid of a standard computer subroutine (LQF in UBC program library). The weights were taken into account. A sample computer output for ALERT BAY i s attached in Appendix 3, The results, as far as they are relevant to this subsection, are listed in Table V. Table V. Amplitude, period and phase lag of seasonal o s c i l l a t i o n Sta.No. Location Period *) n A,SE(A),(cm) T,SE(T),(yrs) M e,SE(Mj,(yrs) 168 Victoria 1909-68 709 8.3 + 0.4 1.0004 + 0.0004 m 0.019 4 0.017 169 Fulford Harbour 1953-68 190 7.3 + 0.7 0.9972 + 0.0032 + 0.146 + 0.197 170 Vancouver 1943-68 310 5.6 + 0.5 1.0010 + 0.0020 m 0.090 + 0.115 171 Point Atkinson 1947-68 260 5.1 + 0.6 0.9988 + 0.0028 0.029 + 0.163 172 Tofino 1943-68 308 12.2 + 0.6 0.9988 • 0.0010 0.071 7 0.059 173 Alert Bay 1948-68 247 10.8 • 0.6 0.9978 + 0.0016 + 0.128 + 0.093 175 Prince Rupert 1943-68 312 10.7 + 0.6 0.9995 + 0.0012 + 0.004 + 0.068 *) n « number of monthly means used 3) Finally for each station the monthly means as computed in step 1 together with the respective regression function obtained in step 2 were plotted on an automatic plotter using standard subroutines. The scale chosen for the horizontal (time) axis i s 1 year » 2 inches and for the vertical (DMSL) axis 1 foot • 2 inches. Inspection of the plots confirmed the computational results. For il l u s t r a t i o n , the plot for ALERT BAY i s shown in Appendix 4^. 3.2.2. Secular variations of DMSL Similarly to the procedure in the preceding subsection, several steps were taken in the study of secular changes. 1) Yearly means of DMSL together with their corresponding weights were computed for each station: 5) Numbers such as, for example, 63.499 or 63.999 on the time axis are due to accumulation of round-off errors in the computer and should be read as 63.5 or 64.0, respectively. . - 25 -The annual means of DMSL were computed from monthly means using the formula z _ j g y j ) y j ) where Zy i s an annual value of DMSL, referred to Chart Datum, for the year Y, Z M ( J ) is the J T H monthly mean in the year Y, WJ^CJ) i s the weight of this monthly mean, and N i s the number of months for which observations are available 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 daily means as a simple mean may amount up to 1 mm (0.003 ft) due to round-off errors. Compared to observational errors, this computational error i s small and i s negligible. The weights associated with annual means were computed from the formula 1 12 where W Y is the weight of the given annual mean for the year Y. Appendix 5 contains a computer l i s t i n g of a l l annual values of DMSL available and their weights for the seven stations considered. 2) For each station, a plot of the annual means was prepared. A horizontal scale of 1 year • 0.25 inch and a vertical scale of 0.1 ft «• 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 for consecutive years only were joined by straight lines. Appendices 6 to 11 are the plots so obtained, completed by regression lines, to be discussed below. - 26 -3) The p l o t s were inspe c t e d . Since the p a i r s of s t a t i o n s VICTORIA and FULFORD HARBOUR, VANCOUVER and POINT ATKINSON are not too w i d e l y separated geo-g r a p h i c a l l y , they were p a i r e d and used f o r comparison. i ) The semi-transparent p l o t f o r FULFORD HARBOUR f o r the p e r i o d 1953-1968 was o v e r l a i d on that f o r VICTORIA f o r the same p e r i o d . The comparison 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 that p e r i o d . The same i s tr u e of VANCOUVER and POINT ATKINSON f o r the p e r i o d 1947-1968. For these 22 years the r o o t mean square d i f f e r e n c e amounts to + 1.2 cm (0.04 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 of the p l o t s and hence t h i s c l o s e agreement f o r the p e r i o d 1947-1968, a root mean square d i f f e r e n c e of + 6.6 cm (0.22 f t ) i s obtained f o r the 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 to 1920 i s c o n s i d e r a b l y g r e a t e r than that s i n c e about 1940. This decrease i n v a r i a t i o n holds f o r s t a t i o n s VANCOUVER, POINT ATKINSON, TOFINO and PRINCE RUPERT. At T0FIN0, f o r i n s t a n c e , the maximum v a r i a t i o n i n the p e r i o d 1914-1920 amounts to 19 cm (0.62 f t ) , w h i l e from 1943 to 1968 i t i s o n l y 12 cm (0.40 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 the bench mark i n f o r m a t i o n a v a i l a b l e , led to the c o n c l u s i o n that records p r i o r to about 1940 are not s u f f i c i e n t l y accurate and are thus not s u i t a b l e f o r computation of a r e g r e s s i o n l i n e . VICTORIA i s an exception s i n c e o b v i o u s l y the gauge was operated c a r e f u l l y and r e c o r d s were processed p r o p e r l y . 4) Using o n l y those records which are 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 order to determine the s e c u l a r v a r i a t i o n . Since no m e t e o r o l o g i c a l data were a v a i l a b l e and s i n c e the i n f l u e n c e o f the nodal t i d e i s n e g l i g i b l y small f o r p e r i o d s of about 19 years or m u l t i p l e s of i t , o n l y the f i r s t term of R o s s i t e r ' s equation (page 17) was used. 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 equations (p - 1) Z y - a Q + a l Y 27 -and q u a d r a t i c r e g r e s s i o n equations (p - 2) a D + a {Y + a 2 Y 2 were computed. A cubic expression (p • 3) was not c a l c u l a t e d because the p l o t s r e v e a l e d no evidence at a l l of a cubic law of change. Estimates estimates were computed by the method of l e a s t squares w i t h the a i d of the computer subroutine LQF. A q u a d r a t i c law of change as w e l l as a l i n e a r one was accepted o n l y i f the standard e r r o r of a 2 d i d not exceed the absolute value of a^ . In June 1946 a severe 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 of the east coast of Vancouver I s l a n d was recorded and became known as the B r i t i s h Columbia Earthquake (Hodgson, 1946). In order to detect p o s s i b l e e f f e c t s of t h i s earthquake, two a d d i t i o n a l r e g r e s s i o n equations were com-puted f o r VICTORIA f o r the p e r i o d s 1909-1945 and 1947-1968. A l s o , to g i v e a b e t t e r comparison with 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. Appendices 6 to 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 to t e s t the s i g n i f i c a n c e of the 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 z y ™ a o + a l Y * I n s t a n d a r d textbooks on s t a t i s t i c s i t i s shown that i f the o b s e r v a t i o n s are Normally d i s t r i b u t e d , the r a t i o of 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 o 1» a 2 0 and the standard e r r o r s of these F ( l , N - 2 ) SE(a,) f o l l o w s the F - d i s t r i b u t i o n w i t h 1 and N-2 degrees of freedom (in the case of weighted o b s e r v a t i o n s N i s equal to the sum of the w e i g h t s ) . Using the above formula, a value of F and the p r o b a b i l i t y a s s o c i a t e d with - 28 -this value were computed. The probability i s that of obtaining an F - value greater than or equal to the one calculated, given that (3 • 0 in the "true" regression equation Z Y - « + (JY . If this probability i s less than 0.05, one may usually conclude that a^ i s significantly different from zero. In other words, the trend i s s t a t i s t i c a l l y significant at the 95% probability level. A sample computer output of a linear regression and the test of significance i s shown in Appendix 12 for ALERT BAY. The relevant findings of steps 4 and 5 are summarized in Table VI (Since SE(a 2) > |a 2l for a l l stations except VICTORIA, a, is given for VICTORIA only). Table VI. Table of regression coefficients Sta.No. Location Period n*> a p SEUj) (mm/yr) ?2», S E£ a2> (mm/yr'') F-Prob. for a^ 168 Victoria 1909-68 60 1.20 + 1.18 + 0.023 + 0.015 1909-68 60 • 0.61 + 0.24 0.01 1909-45 37 0.12 + 0.51 0.80 1947-68 22 + 1.27 + 0.89 0.17 169 Fulford Harbour 1953-68 16 + 1.49 +1.65 0.39 170 Vancouver 1943-68 26 + 2.65 + 0.64 0.00 1947-68 22 + 1.92 + 0.86 0.04 171 Point Atkinson 1947-68 22 2.10 + 0.82 0.02 172 Tofino 1943-68 26 + 0.46 7 0.76 0.56 173 Alert Bay 1948-68 21 0.30 + 1.01 0.76 175 Prince Rupert 1943-68 26 + 2.90 + 0.79 0.00 *) n • number of annual means used 3.3. Discussion of results In order to interpret the results, one f i r s t has to make an assumption about the influence of factors (9) to (13), inclusive, on,DMSL. One may assume that their influence on a monthly and/or annual value of DMSL does not exceed + 3 mm (0.01 f t ) . Based on this 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 in DMSL physically as changes in PSL or PMSL. - 29 -Seasonal variations (changes in PSL) can be expressed numerically in terms of the amplitudes of the seasonal osc i l l a t i o n (Table V, c o l . 5). A minor part of this 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 is due to meteorological effects (factor (2)). The amplitudes range from about 5 cm (0.15 ft) at POINT ATKINSON to about 12 cm (0.39 ft) at TOFINO. This difference in amplitudes at the stations must be considered in conjunction with their geographic positions, and consequently, with different influences of barometric pressure and prevailing winds. It is not surprising that the greatest amplitude is encountered at TOFINO which i s directly exposed to the Pacific 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 air pressure i s f a i r l y well constant over about 250 km (150 mi), this result i s clearly indicative of the great influence of prevailing winds on PSL. The periods (Table V, c o l . 6) are approximately 1 year, but the fact that their standard errors are greater than their deviation from 1.0000 (except for TOFINO and ALERT BAY) seems to indicate a period of exactly 1 year. A similar conclusion can be drawn from the phase lags of the seasonal os c i l l a t i o n (Table V, c o l . 7). Their signs vary between the stations and their standard errors are of the order of their magnitude or even exceed i t . It 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 transition to a new year. Secular variations (changes in PMSL) are expressed in terms of the regression coefficients a^ and} a 2 listed in Table VI, c o l . 5,6. Each of the three regression equations computed for VICTORIA shown in that table and in the plots (Appendices 6,7) has certain advantages: - 30 -1) The computation of a single linear regression equation for the entire period 1909-1968 permits performance of a test of significance 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 linear regression lines for the periods 1909-1945 and 1947-1968 makes allowance for the possible discontinuity in land movement caused by the British Columbia Earthquake of 1946. As shown in Appendix 6, the "jump" in 1946 amounts to 1.2 cm (0.04 ft) and may be due to a sudden r e l i e f of the earth's crust, although nothing definite can be stated because of the relatively large yearly variation. 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 significant. 3) The computation of a quadratic regression line for the period 1909-1968 provides a more flexible continuous description of the geophysical processes involved than does a straight line. Quadratic regressions should always be considered for periods longer than 30 years. For a l l other stations,linear trends were most suitable. The trends are significant for VICTORIA (1909-1968), VANCOUVER (1943-1968), POINT ATKINSON (1947-1968) and PRINCE RUPERT (1943-1968). At a l l these stations a positive secular variation i s observed, thus indicating submergence. Since submergence (as well as emergence) characterizes only a relative movement between PMSL and land, an attempt is made to separate the components of submergence. In doing so, use is made of the following definitions: Relative movement (RM) Sea level movement (SLM) Land movement (LM) + + - + •a Submergence Emergence Rise F a l l U p l i f t Subsidence - 31 -Based on these definitions, the three movements can be related by the equation RM - SLM - LM . Solving for LM yields LM - SLM - RM . In the latter equation the rate of RM is known from the regressions computed above (coefficient a,). The rate of SLM is assumed to amount to +1.0 mm/yr (eustatic rise of PMSL; see factor (7)). The standard error of this rate is estimated to be + 0.3 mm/yr (Montag, 1970). Considering only the four above-mentioned stations with s t a t i s t i c a l l y significant trends, the rates of movements as computed from the relation LM - SLM - RM are listed in Table VII together with estimates of their standard errors. Table VII. Rates of PMSL, relative and land movement Sta.No. Location Period SLM (mm/yr) RM (mm/yr) LM (mm/yr) 168 Victoria 1909-68 + 1.0 + 0.3 + 0.6 + 0.2 + 0.4 + 0.4 170 Vancouver 1943-68 + 1.0 + 0.3 + 2.6 + 0.6 - 1.6 + 0.7 1947-68 + 1.0 + 0.3 + 1.9 + 0.9 - 0.9 + 0.9 171 Point Atkinson 1947-68 + 1.0 + 0.3 + 2.1 + 0.8 - 1.1 + 0.9 175 Prince Rupert 1943-68 + 1.0 + 0.3 + 2.9 + 0.8 - 1.9 + 0.9 Only vague statements can be made about the causes of the land movements given in 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 is of tectonic origin,although the po s s i b i l i t y of local atectonic movements cannot be excluded. Geological studies (Mathews et a l . , 1970) have shown that in southwestern British Columbia isostatic adjustment after deglaciation (factor (5a)) was essentially complete about 8000 years ago. Tectonic movements due to sedimentation may also be disregarded 6) This separation is made possible only by assuming an eustatic r i s e of PMSL at a certain rate. Should new studies of world-wide changes in PMSL result in a better figure for SLM, the new figure would obviously directly affect the rates of land movement shown in the last column of Table VII. - 32 -because of their slow rate (factor (5c)). It is 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 (factor (5b)), provided no atectonic movements have taken place. Further geological studies should c l a r i f y this matter. CONCLUSION Causes and effects of seasonal and secular changes in sea level were covered in section 2 after definitions of sea level were given in the f i r s t section. The main causes for seasonal variations of PSL were found to be barometric pressure and prevailing winds. Tectonic movements of the earth's crust and eustatic changes in PMSL are the main reasons for secular variations in PMSL. In general the factors influencing sea level are of widely different origin and their 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 level can be solved sa 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 for Mean Sea Level) in 1960 was a f i r s t step toward the achievement of this goal. The recent "Symposium on Coastal Geodesy" held by this group (Munich 1970) was another attempt to realize international and i n t e r d i s c i p l i -nary cooperation. As far as possible the results of this meeting were taken into account in this thesis. Section 3 described the numerical determination of seasonal and secular variations in sea level on the coast of British Columbia. The seasonal variation can be regarded as an os c i l l a t i o n with a period of about 1 year, the maximum height of this o s c i l l a t i o n coinciding with the transition to a new year. The average amplitude of this annual o s c i l l a t i o n for seven stations on the - 33 -British Columbia coast amounts to about 9 cm (0.3 f t ) . At TOFINO the os c i l l a t i o n has the greater amplitude (12 cm or 0.4 ft) and is smallest at POINT ATKINSON (5 cm or 0.15 f t ) . Secular changes in PMSL were determined as linear trends of submergence and/or emergence. At VICTORIA, the secular variation can also be represented by means of a quadratic regression line. Except at ALERT BAY (1948-1968) and VICTORIA (1909-1945) submerging conditions are found. The British Columbia Earthquake in 1946 may have resulted in a sudden land subsidence of 1.2 cm (0.04 ft) at VICTORIA. Excluding stations having non-significant trends, the remaining trends of submergence were segregated into movements of sea level and movements of land,assuming an eustatic rise of sea level at a rate of 1.0 mm/yr. There are definite subsidences of land at VANCOUVER, POINT ATKINSON and PRINCE RUPERT during the last 20 years due to tectonic (or atectonic) movements and since 1909, a probable land u p l i f t at VICTORIA. Finally, a few recommendations and suggestions are provided which hopefully w i l l be useful hints for further observations and studies; 1) More permanently operated tide gauge stations should be established along the coast of British Columbia. When selecting sites for additional stations, geophysic as well as hydrographic aspects should be borne in mind. By 1967, 14 permanent stations were already in operation, but this i s s t i l l too small a number on which to base definite conclusions about vertical movements of greater coastal areas. 2) The basic reference for DMSL at any station should be a tide gauge bench mark (T.G.B.M.), connected to several additional bench marks in the v i c i n i t y , but not included in the national levelling net and i t s adjustments. Levelling between T.G.B.M. and the national net then may give evidence of local land movement, but the basic information about DMSL should always be recoverable. It is the practice of the "Canadian Hydrographic Service" - 34 -to use T.G.B.M. as a basic datum (although called Chart Datum) and this practice should not be altered. 3) Tide gauge bench marks should be set according to geodetic standards and in a manner which assures their permanent existence over decades. In questionable cases a geodesist should be consulted. 4) Levelling between tide gauge bench mark and gauging device or devices should be carried out every six months with an accuracy of + 0.5 to 1.0 mm/Vkm , and the results should be carefully recorded. 5) Meteorological data such as a i r pressure, wind velocity and direction and temperature should be recorded (ideally at each gauge station) in 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 tide. - 35 -BIBLIOGRAPHY Dohler, G. (1965). Hydrographic tidal manual. Special publication of the Canadian Hydrographic Service, Ottawa. Doodson, A.T. (1921). The harmonic development of the tide-generating potential. Proc. Roy. Soc. London, A 100, 305-329. Fairbridge, R.W. (1961a). Convergence of evidence on climatic change and ice ages. Ann. N.Y. Acad. Sci., vol. 95(1). Fairbridge, R.W. (1961b). Eustatic changes in sea level. In Physics and Chemistry of the Earth, vol. 4, Pergamon Press. Fairbridge, R.W. (1962). World sea level and climatic changes. Quaternia, Rome, vol. 6, 180-193. Gutenberg, B. (1941). Changes in sea level, postglacial u p l i f t , and mobility of the earth's interior. Bull. Geol. Soc. Am., vol. 52, 721-772. Haubrich, R.Jr. and W.H. Munk (1959). The pole tide. J . Geophys. Res., vol. 64, 2373-2388. Hicks, S.D. and W. Shofnos (1965). The determination of land emergence from from sea level observations in south-east Alaska. J . Geophys. Res., vol. 70, 3315-3319. Hodgson, E.A. (1946). British Columbia Earthquake. J . Roy. Astr. Soc. Can., vol. 40, 285-319. Kalle, K. (1945). Der Stoffhaushalt des Meeres. Probl. d. kosm. Phys., vol. 23, Leipzig. Kuenen, Ph.H. (1955). Sea level and crustal warping. Geol. Soc. Am., Special paper 62. L i s i t z i n , E. and J.G. Pattullo (1961). The principal factors influencing the seasonal o s c i l l a t i o n of sea level. J . Geophys. Res., vol. 66, 845-852. Mathews, W.H. et a l . (1970). Postglacial crustal movements in southwestern British Columbia and adjacent Washington state. Can. J . Earth Sci., vol. 7, no. 2, 690-702. Munk, W.H. and R. Revelle (1952). On the geophysical interpretation of irregularities in the rotation of the earth. Mon. Not. R. Astr. Soc. Geophys. Suppl. 6, 331-347. Pattullo, J.G. (1963). The sea, vol. II: Seasonal changes in sea level. New York, Interscience. Rossiter, J.R. (1962). Long-term variations in sea level. In ( H i l l , M.N. editor) The sea, vol. I, New York and London, John Wiley and Sons, Inc. - 36 -Rossiter, J.R. (1967). An analysis of annual sea level variations in european waters. Geophys. J . R. Astr. Soc, vol. 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 levels along Canadian coast lines. Montag, H. (1970). On the accuracy of determination of secular variations of mean sea level at the Baltic Sea coast. Wemelsfelder, P.J. (1970). Mean sea level 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 daily means of DMSL for ALERT BAY, B.C. ( 1967) DAY MONTH MONTHLY MEAN DAILY MEAN LEVELS NO 173 ALERT BAY B C PST 01 10 1 67 912 937 928 947 914 877 890 917 936 965 11 20 1 67 970 989 963 958 975 908 907 955 1072 1081 21 31 1 67 978 1065 1048 1028 1003 1001 1012 1042 1067 1052 998 NO 173 ALERT BAY B C PST 01 10 2 67 1018 999 991 963 914 906 901 945 942 924 11 20 2 67 950 990 990 974 965 952 968 902 883 907 21 28 2 67 943 890 888 919 964 928 922 951 957 01 NO 173 ALERT BAY B C PST 10 3 67 946 924 923 904 894 874 883 930 936 940 11 20 3 67 926 935 958 971 1002 1039 1015 1003 1009 1019 21 31 3 67 960 978 1041 1036 964 960 961 959 976 967 954 NO 173 ALERT BAY B C PST 01 10 4 67 928 920 930 945 929 901 910 921 921 926 11 20 4 67 956 973 970 946 958 967 947 961 953 925 21 30 4 67 933 919 912 889 892 902 927 949 957 941 916 NO 173 ALERT BAY B C PST 01 10 5 67 916 916 917 909 891 886 894 912 934 932 11 20 5 67 916 897 893 888 892 920 908 893 888 903 21 31 5 67 907 879 879 889 882 877 913 933 962 950 937 NO 173 ALERT BAY B C PST 01 10 6 67 926 950 947 938 937 917 903 912 918 912 11 20 6 67 920 921 902 898 904 922 930 931 935 920 21 30 6 67 916 905 903 896 908 918 920 914 903 893 888 NO 173 ALERT BAY B C PST 01 10 7 67 894 891 923 925 920 909 899 897 888 889 11 20 7 67 891 903 892 898 910 914 923 914 913 896 21 31 7 67 904 891 894 896 896 897 902 916 923 918 913 NO 173 ALERT BAY B C PST 01 10 8 67 897 898 905 899 895 892 877 876 901 923 11 20 8 67 917 918 921 926 922 918 896 869 875 930 21 31 8 67 910 915 909 897 880 903 928 931 943 936 949 NO 173 ALERT BAY 8 C PST 01 10 9 67 983 929 908 915 920 909 931 969 969 1004 11 20 9 67 966 926 913 916 917 932 925 902 924 942 21 30 9 67 939 951 911 927 953 930 935 963 962 973 964 NO 173 ALERT BAY B C PST 01 10 10 67 978 975 961 951 973 997 1009 1022 1007 1034 11 20 10 67 996 955 960 882 889 882 930 929 909 960 21 31 10 67 961 1010 1010 933 994 944 „ 958 1032 966 920 938 NO 173 ALERT BAY B C PST 01 10 11 67 862 873 910 943 968 986 984 1007 1012 1022 11 20 11 67 944 944 951 974 936 926 966 937 919 923 21 30 11 67 944 937 935 940 934 885 873 915 955 980 966 NO 173 ALERT BAY B C PST 01 10 12 67 998 1044 1068 1086 1061 1068 1049 1007 1023 988 11 20 12 67 912 877 862 865 904 917 954 948 938 931 21 31 12 67 955 947 980 949 932 932 910 891 868 881 898 HIGH LOW DAY HR HT DAY HR HT 1001 27 1340 1810 9 1905 137 24 1246 1708 25 2034 97 938 28 232 1785 28 905 205 26 151 1734 26 845 62 918 "24 32 1702 25 852 15 22 907 21 977 20 1667 23 836 13 1592 21 739 129 1610 7 838 77 119 117 ! 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 com-puted 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 avail-able, 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 for ALERT BAY, B.C. (1948 - 1968) r NC 1 7 3 A L E R T E AY B C M C N T H MMEAN ^ W E I G H T AS.46 9.27 . 1 .OQ 4 8.54 9.20 1.00 48 .63 9.26 1.00 48.71 c.. 34 1.00 48.79 9.29 1 .00 48 .88 9.48 1.00 ,48.96V 9.75 vvi . .oc r NC 173 A L E R T - E AY a c •' jj'^V '• MONTH MMEAN W E I G H T 9.10 1.00 49.13 9 . 81 l.CC 49.21 9.68 1.00 49.29 9.31 1. 00 49.38 9.32 1.00 49.46 9.08 1.00 49.54 "9*0.2". 1 .00.' 49. 62 9.27 1 .00 4 9.71 9.25 1 .00 49.79 9.02 1.00 49.fi? 9.73 L O G 49.96 9.49 1.00 #*v.' NO 173 A L E R T BAY B C '^•"r MONTH W E I G H T 50.04 9.41 1.00 50.13 9.72 l.CC 5C.21 9 .69 l.OC "50r.l9" 9.41 1.00 50.3 8 .'. 8 .97 l.OC !' '• 1.00'fc.fW*^'; 50; 63 9..2 0 1.00 50.71 9.18 1.00 50.79 9.85 1.00 50.88 9.79 1.00 50.96 10. 06 LOO N C 173 A L E R T BAY B C n !u' 'if'') M C N T H M N E A N W E I G H T 51.04 9.76 •1. CC 51 . 13 9.73 1. CO 51.21 9.27 • 1.00 5 1.29 9.00 1. CO ~ 5 T 7 I 7 _ 9.23 1 . 0 0 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 9.92 1 .00 'Tf.96 9.68 1.00 N C 173 A L E R T BAY B C M O N T H . NMEAN W E I G H T 52.04 10.14 1.00 52.13 9.76 1.00 52.21 , 9.47 l.CC 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 NC 17 3 A L E R T BAY B C : M O N T H •MMEAN W E I G H T 53.04 ' 10.28 1.00 53.13 ' 9 .3.5 1.00. 5 3.21 9.51-1.00 5 3. 29 9.27 i . c o 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 NC 173 A L E R T EAV e c • MONTH M N E A N W E I G H T 54. 04 10.0 6 1.00' 54 .13 10 .01 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 54.71 9.30 l.OC 54.79 9. 50 1.00 • 54.88 9 .98 1.00 54 .96 10.10 1. CO N C 173 A L E R T E AY e c I' MONTH MMEAN W E I G H T 55.04 9.64 1.00 55.13 1 .00 55.21 9.02 ~~ 1 .00 55.29 S.42 1.00 55.38 8.90 1 .00 55.46 9.05 1.00 55.54 9.15 1.00 55.63 8. 9-l.OC 55.71 9.07 l . O C 55.79 9.37 l.CC 55. 86 9.51 l.CC 55.96 9 .96 1.00 N C 173 A L E R T E AY e c ' • • ' . . . . MONTH MMEAN W E I G H T 56.04 10.22 1.00 56. 12 9.45 1.00 56.21 ' 9.4 5 1 .00 ' ~5T.~29" S. 16 i . c o 5.6.38 56.46 9. 34' l.p:0.' 56 .54 -, .9.10 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 NC 173 A L E R T E AY e c • ,r MONTH MMEAN W E I G H T 57.04 9.26 1 . 0 0 57.13 9.39 1 .00 57.21. 9. 58 : .1.00 c.. 25 1.00 57. 3^ 8 9.41 1 vOC 5 7.46 9.24 I.CO 57.54 9.26 1.00 57. 6 2 9.31 1. OC 57.71 9.40 l.CC 57.79 9.49 l.CC 57.86 9.47 l.CC 57. 96 10.14 l.CC Nt 173 ALERT E AY B c MONTH 58 .04. • 5 8. 13 5 8.,21 5 8. 29 58.38 .58 .46 58 .54 58. 63 58.71 58. 79 58. 88 58 .96 MMEAftf 10 .20 10. 4 7 9.65 c 59 9.16 9.32 9 . 16 9. 32 9.45 9. 56 9. 63 9 .92 WEIGHT 1 .00 1 • CO 1 .00 1 . 00. - 1.00 1 .00 1 .CO 1. O C LOO 1. CO 1. CG 1 .00 NC 173 ALE Ft E AY e c ' • " MONTH . •'A.. 59 .04 59. 13 59:21" 5 9. 29 59.38 59.46 59 .54 59. 63 59.71 59. 79 59. 8 8 59 .96 MMEAN 10 .02 9. 81 9 . *&• v c;. 15 9.11 9.27 9 . 0 0 9. 11 9.44 9. 33 9. 20 9 .66 KE I'GHT; '. .-;,i .00 1. 00 1 .00" ;'-'\\ 00 1 .00 1 .00 1 .00 1. OC 1.00 1. GC 1. OC 1 • CO ,A^ ..NC 1 7 3 A L E R T . E A Y „B C " - » - ~ - V « W * T ; -> ! ^ V > ' ; MM E A N V " . WEICHT 60. C*? 9.73 1 . 0 0 68.13 9.6 6 .1 .00 60.21 9.46 1.00 60.29 9. 53 1.00 V 60.38 9.46 1 . 0 0 60.46. 1 60 .-64 8.198 A 1.00 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 NC 173 A L E R T B A Y 8 C i MCNTH M M E A N W E I G H T 6.1. C4 9. 99 1.00 61.13 10. 04 1.00 61 .21 10.03 1.00 61 .29 9.17 1.00 61.38 9.25 1.00 61.46 9.19 1.00 61.54 9.07 l.CC 61.63 9.17 . L O G 61.71 9 .10 1 . 0 0 61.79 9.18 1.00 61.8 8 9.35 1.00 61.96 9.54 1.00 NC 173 ALERT BAY B C . .  KChTH 62.04 62.13 62.21 62.29 62.38 62.46 62.54 62.63 62.71 62.79 62.88 62.96 MMEAN . ;9. 33 9. 67 9.26 9.12 9.03 8.98 8.94 9.'26 ' 9.31 9.79 9.90 9.88 HEIGHT 1.00 l.CC LOG LOG l.CC 1.00 l.CC l.CC 1.00 l.CO 1.00 LOO NO 173 ALERT BAY 8 C MC NT H MMEAN WEIGHT 63.04 9. 19 LOO 63 .13 9. 90 1.00 63.21 9.34 1 .00 6 2.29 S.68 l.GG 63.38 9.39 l.GG 6 3,46 9.15 1.00 63.54 9 .30 l.GG 6 3.63 9.17 LOG 63.71 9.57 1.00 6 3. 79 9.90 1.00 63.88 10.11 1.00 63.96 9.86 1.00 NO 173 ALERT BAY 8 C * > KG NTH MMEAN WEIGHT 64.04 ' 10. ].5 1.00 64. 13 9. 04 l.CC 64.21 9.22 LOG 6 4.29 8.83 1..C0 64.38 8.90 LOG 64.46 9.14 1.00 64.5 4 ' 9.21 1.00 64. 63 9.22 1.00 64.71 9.13 l.CO 64. 79 9.25 1.00 64.88 9.51 1 .00 64.96 9.83 1 .00 • , NC 173 ALERT BAY B C ^ - f ^ % ' ?»>• " •••,U- MONTH 65.04 6.5 .13 65.21 65.2~9 . .65.38 6 5."4^F^v54 6 5.63 6 5.71 65.79 65.88 65.96 MMEAN 9.74 r{/9>.35 .9.13 9.36 8.87/.. 8...9^ 4,'.^ .07 9.29 9.12 9.59 10.04 10. 04 8...?^'..;^s?.07 i.#-SHilbo w E 1 G H VrJ'J 1* 0 c .l.CC LOG: 1 i . e c 1.00 1. G^-''i^.op 1.00 1.00 1.00 1.00 1.00 NC 173 ALERT BAY B C MCNTH 66.04 66 .13 66.21 6 6.29 66.3.8;.. 66.46 66. 54 66. 6 3 66.71 66.79 66.88 66.96 NKEAN 9.89 9.63 9.65 9.02. 8.82 9.17 9. 1.1 9.25 9.26 9.62 10.09 WEIGHT 1.00 ' -1 .OC l.CC .-,1:.CC l.'CG .':,'L'V:00 ;'l'.OQ 1.00 1.00 1.00 LOO 1.00 NC 173 ALERT BAY B C ____. :  MCNTH 67.04 67.13 67.21 6 7.29 '6,773 8 ~67.46 67.54 67.63 67.71 67.79 67.88 67.96 MMEAN 9.78 9.43 9.60 .9.33 9.07 9.16 9.05 9. 10 9.3S 9.61 9.44 9.55 WE IGHT l.CC -LOG 1.00 l.CC r.OO. 1.00 1 .00 .1.00 1.00 1.00 1.00 1.00 NO 113 ALERT BAY B C K M h 68.04 .68 .13 68.21 MMEAN 9.81 9-84 9.72 WEIGHT l.OC 1.00 1.00 66.29 68.26 68.46 68.54 8.95 9.13 9.00 9.i0 l.OC 1.00 1.00 1.00 68.63 68.71 68.79 68.88 68.96 9.33 9.23 9.64 9.85 9.94 I .00 1.00 1.00 1.00 1.00 APPENDIX 3 Sample computer output of least squares f l of monthly means of DMSL to the function Z M - a0+ a,M + A cos [2l?/T(M - M0)] for ALERT BAY, B.C. < 5 , STAT I C N NC 1 7 3 A L E R T b AY B •v ~. ' , r >\ s -A ^ y "/v:y *• . •,.-»*-.•. * \ ? I N T E R M E D I A T E E S T I M A T E S CF P A P A ^ E ' T E P S , SLA-9 . 5 C C C < 0 . 0 ' " C . 3 5 C O C ^<=.5ic.t - - C . 1 5 6 2 2 E - C 2 C . 2 5 2 7 7 CF S C L A R E S ' * l . c c c b " ' f . 9 9 7 7 9 c . 0.. c 1 2 9 4 9 1 4 . 4 9 4 1 2 . 7 1 5 9 . 5 C 9 4 9 . 5 C 9 4 9 . 5 C 9 4 - C . 1 5 5 7 5 E - C 2 . - C . 1 5 5 8 6 E - C 2 - C . 1 * - R £ 6 E - C ? , , . C . 3 5 3 9 5 C . 2 5 2 9 5 C . , 3 5 3 9 5 - C c 9 7 84 C . 9 9 7 8 3 0 . 9 9 7 8 3 0 . c. 0 . 1 2 7 4 6 1 2 8 C 1 1 2 7 9 8 1 2 . 7 1 4 1 2 . 7 1 4 1 2 . 7 1 5 9 . 5 C S 4 * c 9 . 5 C 9 4 . 9 . 5 094 - • - C . 15 5'8 6 E - C 2 - v .-;rO,.I558 6 E - 0 2 - • » . > G 4 1 5 5 6 . 6 E - 0 2 C . 25 2 9 5 0 . 3 5 39 5 C 3 5 3 9 5 ' G . 99783 ] . .•<:i,,0.9 9 7 8 3 ; • - v ^ i 0 i 9 9 7 8 3 l -c . 0 . 0 . 1 2 7 9 8 1 2 7 9 9 1 2 7 9 9 1 2 . 7 1 4 1 2 i 7 l 4 1 2 . 7 1 5 • 9 . 5 0 9 4 • .. 9.5C^4 ;;::'U':.' .•-0:*:X5 : 5'84E-C2 '.' ^ '0Vl5'5l :6' :E-O2,-. •KT?.} -C . 3 5 2 9 5 0 . 3 5 39 5 •riryf^);^: 0 . 9 9 7 8 2 c . c . 1 2 8 0 1 1 2 6 0 2 1 2 . 7 1 5 1 2 . 7 1 4 F I N A L ESFI-KATES->::e'F:;-;^;ARAME;TERS • " ,-9 . 5 0 9 4 ' '>,»-~0..a:55 ;8 r5 £ - 0 2 - -A = 0 . 3 5 3 9 5 1 - 0 . 9 9 7 8 3 NC M„= 0 . C F I T E R A T I O N S 12 8 0 0 10 SUM C F S CU AR ES 1 2 . 7 1 4 '»{*!-, 4 C tf- ' E S T I M A T E S OF S T A N D A R D (E'£R0i-,:J0 THE P A R A M E T C . 1 4 4 8 5 0 . 2 % f ^ $ ^ 0 * 2 G . 2 0 577.E 0 .1570:5 E - 0 2 0 . 9 2 7 0 5 E - O 1 = SE(T). ' T I ME(MjDNTH) 4 8 . 4 6 MEAN SEA L E V E L 9 . 2 7 WE IGHT l . C C T I T TED MSLX, E , 9 . . l € 7 , : ' ;^ ' 4 6 . 5 4 4 8 . 6 3 4 8 . 7 1 ; 9 . 2 0 9 . 2 6 9 . 3 4 r.oo; • . l . CC . :• 1.0 0 ' '. 9 . 0 8 2 1 9 . i 5 7 . 9 . 2 9 9 • .4 4 6 . 7 9 4 8 . 8 6 48 . 9 6 ;'.>' 9 . 2 9 . • ' ; ; 9 . 4 8 • • 9 . 7 5 1 . 0 0 . . l l.OC ?>V.OC 9.•473 -jv;.-- ..• 9 . c 5 6 ;-;:fy|r . 9 . 7 6 1 ;• ® " 4 9 . 0 4 49 . 13 4 9 . 2 1 9 . 1 0 9 . 6 1 9 . 6 8 1 . 0 0 l . O C l . O C 9 . 7 8 5 9 . 70 7 9 . 5 6 5 . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • * • • • « • • • • • • • . - . 6 8 . 2 9 6 8 . 3 8 6 8 . 4 6 6 . 9 5 • 9 . 1 3 9 . C C " l . O C I . 0 0 . i . c o ,: , 9 . 2 7 2 9 . 1 1 6 9 . 0 5 1 J 6.8.54 ' •'*68x.'63 X-**./.. 6 8 . 7 1 9 . IC 9 . 3 3 . 9 . 2 2 .... ^ l . O C • •" .'. i .OQ ; v ; ,^ :.1 9 . C 7 4 .;• 9 . 1 9 6 T -9 43b i • ,.v:;;J,.,.: • • ;:4.8 . 7 9 . • •' • 6 8 . 8 8 • 6 8.96 ' - -' • 9 . 6 4 - • • 9 . 8 5 ,9 .^4 , - ' i f coc . ••.'"'i:.o0i'-; *>-51.d0.r/ • . 9 . 5 3 6 • •'-•-« " ; 9 . 6 9 1 ' . 9 . 7 5 4 - . - WEIGHJT%0 : M E A N 9 . 4 162 -''.Str = 2.47.;.6o:-'>:'-' " .":*'' '.i'..;\.v»';"fr.V" • " - * YJ* APPENDIX 4 Sample p l o t of monthly means of DMSL f o r ALERT BAY, B.C. and function f i t t e d to them APPENDIX 5 Listing of annual means of DMSL ***** STATICN NC 168 VICTCPIA E C ***** ANNUAL MEANS OF DMSL - 48 -YEAR OMSK FT ) WEIGHT 19 9 1910 1911 5.976 6. G26 6 .080 0 . 87 1. CC 1.00 1912 19 13 1914 6.G7C 6.C4 5 6.299 1 . 0 0 1 . 0 0 1.00 1915 1916 1917 6.23 8 6.002 5 .915 1 . 0 0 l.CO 1.00 1918 1919 19 20 6 .194 6.G6 8 6 .050 1 . 0 0 1 . 0 0 1 . 0 0 . 1921 1922 1923 6.101 5*987 6 .081 1 . 0 0 l.CC 1 . 0 0 19 24 1925 1926 6.021. 6.16 5 6.122 1 . 0 0 l.GG 1 . 00 1927 192 8 1929 6.179 6. 120 5.919 1 . 0 0 l.CC l.GG 1930 1931 1932 6.159 6. 19 5 6.178 1 .00 1. CO 1.00 1933 19 34 1935 5.981 6.012 6.029 0 .58 C. 5 8 1.00 19 2 6 1937 1938 5.897 6.014 5 .941 0 .99 l.OG l .CO 1939 19 40 1941 5.947 6. 215 6 .369 1 . 00 l.CC 1 . 0 0 194 2 1943 1944 6.C9 8 6. C58 5.978 1 . 0 0 l.CO 1.00 1945 1946 194 7 6.C47 6.C92 6 .072 1 . 0 0 l .OG 1 . 00 = - ; --1948 1949 19 50 6.172 6.€21 6 .153 1 . 0 0 l.GG 0.9 3 19 60 1961 196 2 6.C9 1 6. 159 6 .064 l.CC:,:.-' : • - . : " l i O C '•' > i.eo 19 51 19 52 19 53 6.183 6.14 2 6 .189 1 . 0 0 l.CO 1.00 IS 63 ' 19 64 1965 6.226 6.G59 ' 6.20 5 l.CO 1 . 0 0 •1 .00 1954 19 55 1956 6.24 3 6.G12 6 .081 1 . 00 l.CC 1 . 0 0 i 19 66 1967 1968 6. 189 6.206 6.295 . l.GG'.. l.CC' 19 5 7 19 58 19 59 6.190 6. 37S 6 .13 8 1 . 0 0 l.GG 1 . 0 0 1 ^ ^ f f Jl"'*"^-y-'... 'V, - 4 9 -4 * 4 * * STATION NO 169 FULFORD FBR 8 C ***** ANNUAL MEANS CF DMSL YEAR DMSL(FT) WEIGHT 19 53 19 5 4 19 55 7 .391 7.451 7. 229 1 . 0 0 1.00 l . C C 1956 19 57 19 5 8 7.294 7.416 7.618 C .86 0 .99 l.GG 1959 1960 1961 7.420 7.373 7.427 1 . 0 0 1 .00 1.00 19 62 1963 1964 7.295 7.510 7.281 l.OG 0.92 l.OG 196 5 1966 19 67 7.417 7.434 7.440 1.00 1 .00 l.OG 19 6 8 7 .532 G.9 5 * * * * * STA T I CN NO 1 7 0 V A N C C U V E R B C * * * * * ANNUAL MEANS OF CNSL - 50 -YEAR DMSL(FT ) WEIGHT 1910 1911 1912 9.92 1 9.98 6 10 .03 2 C.9C 1.00 1 . 0 0 -1913 1914 1915 10. C 7 6 10 -194 10.157 l.OG l.OG 1 .00 1916 1917 1918 9.922 9.856 10.15 7 0.43 0.9S 1 . 0 0 1919 1920 1921 10.G62 10.02 1 10 .096 l.OG ' l.CC 1.00 1922 192 3 1940 9.97C 10.025 10.106 l.CC 1.00 0.97 19 41 194 3 1944 10.22C 9.646 9.79 7 l.GG l.CC 1.00 194 5 1946 1947 9. 881 9.912 9 .897 l.CC 1.00 1 . 0 0 1948 1949 1950 10.CC9 9-862 10.054 l.CO l.OG 1 .00 19 51 1952 1953 10.04 6 9.982 10 .027 l.GG 0.98 1 .00 19 54 1955 1956 10.CSC 9.84 2 9.937 l.OG l.CO 1 .00 19 57 1958 1959 10.0 22 10.200 9 .990 l.CC l.CC 1 .00 1960 1961 1962 9. 964 10.0 3 6 9.941 1.00 1.00 1.00 1963 1964 1965 10.09 7 9 .9 6 7 10 .061 C.S 6 1.00 1 .00 1966 19 67 1968 IC.14C 10.059 10.167 0.81 l.OG 1 .00 * * * * * S T A T I O N NO 171 PC INT A T K I N S C N B C * * * * * ANNUAL MEANS OF CMSL - 51 -YEAR D M S L i FT ) WE IGHT 1 9 1 4 1 9 1 5 1 9 1 6 1 0 . 1 3 8 10 . C82 9 . 9 0 4 0 . 6 7 1.00 1.00 1 9 1 7 1 9 1 6 1 9 1 9 9 . 8 5 7 1 0 . 1 2 7 9 . 9 0 5 1 . 0 0 l . C C 1 . 0 0 19 21 1 9 2 2 1 9 2 7 9 . 9 8 4 9 . 6 7 8 9 . 8 4 3 1 . 0 0 0 . 3 7 1.00 1 9 3 2 1 9 3 3 1 9 4 4 10 - 0 81 9 . 9 4 7 9 . 7 9 8 0 . 0 8 1. CC 1 . 0 0 1 9 4 5 19 4 7 1 9 4 8 9 . 9 7 7 9 , 8 9 8 1 0 . 0 5 0 1 . 0 0 1 . 0 0 1 . 0 0 1 9 4 9 IS 5C 1 9 5 1 9 . 9 3 8 1 0 . 1 5 6 10 . 1 5 2 1 . 0 0 1 . 0 0 l . G G 19 52 1 9 5 3 1 9 5 4 1 0 . 0 9 7 10 . 1 2 3 10 . 2 1 5 1 . 0 0 1 . 0 0 1 . 0 0 19 5 5 19 56 1 9 5 7 9 . 9 7 7 1 0 . 0 3 6 10 . 1 6 9 1 . 0 0 1 * 0.0 1 . 0 0 1 9 5 8 1 9 5 9 1 9 6 0 1 0 . 2 4 5 1 0 . 0 9 7 10 . 0 4 7 0 . 5 7 0. 90 1.00 1 9 6 1 19 62 1 9 6 3 1 0 . 1 5 4 1 0 . 100 10 . 1 9 1 1 . 0 0 C . 9 6 1 . 0 0 1 9 6 4 19 6 5 1 9 6 6 1 0 . 0 4 7 10. 126 10 . 1 51 1 . 0 0 l . O C 1 . 0 0 19 67 1 9 6 8 1 0 . 1 5 9 1 0 . 2 5 8 1 . 0 0 1.00 ***** STATICN NO 172 TOFINO B C ***** ANNUAL MEANS OF CP SI - 52 -YEAR OPSLCFT) WEIGHT 1910 1911 1912 7.352 7.217 7.242 l.OO 1.00 l.GG 1 9 1 3 1914 1915 7 .307 7-53 6 7.4 28 1.00 1.00 1.00 1916 1917 1918 7.194 7.296 7.247 0.75 0 . 17 1. CC 1919 1920 19 40 7 .124 6.917 7 .269 1.00 0.88 l.OC 1941 1943 1944 7 .373 6.990 6 .939 1 .CO 1.00 l.CC 1945 1946 1947 6 .9 21 6.969 7.052 1.00 0.92 0.86 1948 1949 19 50 7.110 6 .90 5 7 . C 5 7 1.00 1 . 0 0 1 . 0 0 1951 19 52 19 53 7.027 7.G19 7.024 1 . 0 0 1.00 C.7 6 1954 19 5 5 19 56 7 .136 6.819 6.926 l.OC 1.00 I.CO 1957 19 58 19 59 7 .080 7.218 6.9 26 1.00 1 .00 l.OC 1960 19 61 1962 6.995 7.042 6.926 1 . 0 0 1.00 l.CC 1963 1964 19 6 5 7 .095 6.829 7.022 1.00 1 . 0 0 l.OC 1966 19 67 1968 7".02 2 7.003 7.136 l.OC 1 . 0 0 l.CC 4 * 4 * 4 S T A T ICN NO 173 A L E R T BAY B C * * * * * ANNUAL MEANS OF DNSL - 53 -YEAR D M S L ( F T ) WEIGHT 1 9 4 8 1 9 4 9 19 50 9 . 3 6 9 9 . 3 4 1 9 . 4 6 6 0 . 58 1 . 0 0 1 . CC 1 9 5 1 1 9 5 2 19 53 9 . 39 7 9 . 4 3 3 9 . 5 1 0 1 . 0 0 l . G G 1 . 0 0 1 9 5 4 1 9 5 5 1 9 5 6 9 . 5 5 4 9 . 2 8 0 9 . 3 3 4 1 . 0 0 1 . 0 0 1 . 0 0 1 9 5 7 1 9 5 8 1 9 5 9 9 . 4 3 2 9 . 6 1 8 9 . 2 7 9 1.00 1.00 l . C C I 9 6 0 1961 1 9 6 2 9 . 3 9 0 9 . 4 2 3 9 . 3 7 2 1.00 1 . 0 0 1 . OC 1 9 6 3 1 9 6 4 19 65 9 . 5 4 7 9 . 2 86 9 . 3 7 8 l . C O 1 . 0 0 1.00 .._ _ 1 9 6 7 1 9 6 8 9 . 3 8 0 9 . 3 7 6 9 . 4 6 2 l . C O 1 . 0 0 1 . 0 0 ***** STATICN NC 175 PRINCE FU PERT E C ***** ANNUAL MEANS OF DMSL - 54 -VE AR DMSL(FT ) HEIGHT 19 9 1910 1911 12.45C 12.484 12 .407 0.92 C.61 0.5 2 1912 19 12 1914 12.432 12.666 12.814 0. 92 1. CO 1.00 1915 1916 1917 12 .63 8 12.295 12.385 1 .00 l.OC 1.00 1918 19 19 19 21 12.503 12.8C8 12 .413 1 .00 0.25 0.83 19 2 2 1924 19 27 12.415 12.352 12 .426 Q.17 l.CG 1.00 1939 19 40 1941 12.520 12.657 12.70 6 1 .00 l . C C 1.00 1943 1944 1945 12.44 7 12.452 12 .424 1 .00 1.00 1.00 19 46 1947 1948 12.44 6 12.399 12 .498 1 .00 1.00 1.00 1949 19 50 19 51 12.415 12.45 1 12.33 3 1 .00 1. c c 0.92 19 5 2 1953 19 54 12.57 5 12.7 27 12.714 1 .00 l.OC 1.00 19 55 1956 1957 12 .456 12.473 12 .544 1.00 1.00 1.00 1958 19 59 1960 12.713 12.617 12.642 1 .00 0.9 7 0.95 1961 1962 1963 12.63 2 12.478 12.733 1.00 1. GG 1.00 1964 1965 1966 12.564 12.490 12 .640 1 .00 1.00 1.00 1967 1968 12.564 12.786 1 .00 1.00 APPENDIX 6 Plots of annual means of DMSL for VICTORIA,B.C. and FULFORD HARBOUR, B.C. and linear regression lines - 57 -APPENDIX 7 Plot of annual means of DMSL for VICTORIA, B.C. and quadratic regression line APPENDIX 8 Plots of annual means of DMSL for VANCOUVER, B.C. and POINT ATKINSON, B.C. and linear regression lines - 61 -APPENDIX 9 Plot of annual means of DMSL for TOFINO, B.C. and linear regression line - 63 -APPENDIX 10 Plot of annual means of DMSL for ALERT BAY,B.C. and linear regression line - 65 -APPENDIX 11 Plot of annual means of DMSL for PRINCE RUPERT, B.C. and linear regression line - 6 7 -APPENDIX 12 Sample computer output of l e a s t squares f i t of annual means of DMSL to the f u n c t i o n Z>_- a 0+ a,Y with t e s t of s i g n i f i c a n c e f o r a, f o r ALERT BAY, B.C. V #«*** STATION NO 173 ALERT BAY B C v "• • J: ';*:,• :': - 6 8 -r . • I.N T E F;M EC I AT E EST IM AT ES CF PAPAMETEFS, SUM OF •SQUARES c o . v ' o . o 1861 .9 FINAL ESTIMATES OF PARAMETERS -.: i 9.4727 -0.97179E-03 SUM CF SQUARES 0.14954 ESTIMATES CF STANDARD ERROR OF TF E PARAMETER $ • ' i C. 19159 0.32747E-02 * FRATIC FOR PARAMETER 2 = 0.C881 FPROB FOR PARAMETER 2 = C.7623 TIME,YEARS) MEAN SEA LEVEL WEIGHT FITTED MSL 48.G 9.369 0.5 8 9.4260 49.0 9.341 1 .00 9 . 4 2 5 C 50.C 9.466 1.00 9.4241 51.C 9.39 7 l.CC 9 . 4 231 52.0 9.433 1.00 9.4221 5 3.0 9.510 1 .00 9.4212 54.0 .9.5 54 1 .OC 9.4202' 55.0 9.280' 1 .00 9.419 2 56.0 9.324 1 .CO 9.4182 57.0 9.4 2 2 1 .00 9.4173 58 .0 9.618 1 .00 9.4163 . '. 59.0 9.379 1 . 0 0 9.4153 60.C 9.390 1.00 9.4143 61.C 9.423 1 . 0 0 9.4134 62.C 9.27 2 1 . 0 0 9.4124 63.0 9.547 1.00 9.4114 64.0 9.286 1 .00 9,4105 65 .0 9.378 1 . -00 9.4095 66.0 9.3 80 1 .00 9.4085 ' • 6 7.0 9.37 6 1 .00 9*4075 • . 68.0 9.463 1 .OC " •9.40 66: jgi. . • WEIGHED MEAN = 9.4 166 SUM. = 2C.5 8 ; • '- . i t VI" 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050565/manifest

Comment

Related Items