Tides and their seminal impact on the geology, geography, history, and socio-economics of the Bay of Fundy, eastern Canada.
By Gordon Fader
From the earliest European exploration of the New World in the 17th Century, mariners have been acutely aware of the extreme high tides and associated strong currents of the Bay of Fundy. Indeed the region is known internationally for tides that can reach 15 m or more in height and expose vast expanses of seabed during low water. Local tourism actually invites potential visitors to come and walk on the ocean floor. For those who go down to the shoreline, knowledge of the rising tides is an essential survival tool, as in places these tides can literally outrun those who venture too far offshore.
Recent interest and debate in both the Canadian and global press has focused on whether the tides of Fundy are indeed the highest in the world as claimed by many in Atlantic Canada. The title is also claimed by communities in Ungava Bay, northern Quebec. However, recent research by the Canadian Hydrographic Service indicates that the Fundy tides likely outrange those of Ungava Bay by just a few centimetres. But to be fair, the margin of error is greater than the difference, and appropriate data for a meaningful comparison do not exist. Of course, the ultimate question is: why does the Bay of Fundy have such high tides? Surely it can't be just the narrowing shape and shoaling of the bay. And how long have these tides existed: are they a relatively new phenomenon of postglacial emergence? And perhaps more importantly, will the tides change in the future with rising water levels? The development of coastal areas through continued urban sprawl and the maintenance of large areas of dykeland depend on such an understanding.
But there is more to the tides than just an elevational shift of water. These tides drive much of the richness of the Fundy and Gulf of Maine ecosystem through movement of over 100 cubic kilometres of water into the Bay each tidal cycle. Such a massive exchange thoroughly mixes the waters and greatly increases productivity, a process that extends well out into the Gulf of Maine. These nutrient-enhanced fast-moving waters nourish rich fisheries in the Bay and Gulf, particularly with regard to sea scallops, and provide for a substantial sustainable economic return for the region. Recent seabed mapping has discovered large areas of the floor of Fundy covered in unique linear mussel bioherms never before seen on the adjacent Scotian Shelf. Even migrating shorebirds, such as the semipalmated sandpiper, depend on Fundy tides and associated vast mudflats for the provision of essential food to support their long migration from the Canadian North to South America. On the other hand, the Fundy tides result in a cooler climate for the region. For those who live in Nova Scotia's Annapolis Valley, a trip to the Fundy shoreline is a welcomed relief from oppressive summer heat. In contrast, in winter strong westerly winds that blow across the Bay often pick up moisture and produce large local snowfalls ("Fundy flurries") in the Annapolis Valley.
The fast moving waters clocked at over 16 km per hour at Cape Split in the inner Bay of Fundy have also produced dramatic effects on the seabed. Extensive desert-like sand dunes cover many areas, and in Chignecto Bay and Minas Channel constricted areas are scoured down to bedrock in depressions as deep as 60 m. I have always said that if you want to experience the wrath of God, take a hike to Cape Split, a new provincial park at the eastern end of North Mountain, Nova Scotia, and stand at the edge of the 100 m cliff at the time of maximum tidal flood. There you will observe impressive roiling and boiling of the sea, with the generation of large vortices, as the ocean becomes river-like in its inward surge.
Having led many scientific expeditions to study the marine geology of the Bay of Fundy, I am always amazed by the unique and rapidly changing environmental conditions there, and their imprint on the seabed. Once, while we were attempting to run a seismic traverse through Minas Channel at slack water, the CCGS Hudson, although traveling at 5 knots, was actually moving backwards. With expensive gear towed behind the vessel I was very worried and not sure what to do in this circumstance so forged ahead at gear-shattering high speed. As we began to escape the clutches of the high current of the channel just off Cape Split, a large oceanographic gyre located in Scots Bay literally shoved the entire ship to the north in an instant. To top it all off a violent thunderstorm raged while all this was going on.
This synthesis report presents a comprehensive anatomy of the Bay of Fundy and its world-class tides. The work is the result of a long collaboration between Con Desplanque and David Mossman. From the beginnings of postglacial high tide development, perhaps 8000 years ago, the authors describe in detail the many physical factors that play a role in the formation and characteristics of the tides, including the dominant near-resonance length of the Bay of Fundy. The influence of geography, morphology, and gravitational forces of the Sun and Moon, as well as a summary of the geological origin of the Bay and a history of its tides, are all expertly presented. Unique characteristics arising from the high tides, such as tidal bores and reversing falls, are part of the synthesis, as are the age-old dream of electricity generation from Fundy tidal power and the unique conditions of severe winter ice. The ever-present hazard potential from combined high tides and storm surges is evaluated with evidence from the great Saxby tide of 1869 and the Groundhog Day storm of 1976.
This publication is a must for oceanographers and oceanographic students who want to understand how geography, geology, and oceanography can combine in unique ways to produce such high tides and energy rich events. Those interested in the history and environment of the region will find the paper of particular interest as the tides play a critical role in defining the characteristics of the coastal zone. Engineers who must develop structures in such a coastal zone will see how humankind has attempted to mitigate the effects of such a dynamic system and what some of the predicted and unpredicted results can be. The tides of Fundy truly play a dominant role in the physical, chemical, and biological processes of the region.
The production of synthesis reports like this is becoming more of a rare event, as the modern applied science approach limits opportunities for such a thorough and integrated study. This publication will indeed serve as a definitive benchmark study of the region with the "World's Highest Tides".
Tides are an ever-present reality in many coastal regions of the world, and their causes and influence have long been matters of intrigue. In few places do tides play a greater role in the economics and character of a region and its people than around the shores of the Bay of Fundy in eastern Canada. Indeed, the Bay of Fundy presents a wonderful natural laboratory for the study of tides and their effects. However, to understand these phenomena more fully, some large perspectives are called for on the general physics of the tides and their operation on an oceanic scale. The geologic history of the region too provides key insights into how and why the most dramatic tides in the world have come to be in the Bay of Fundy.
Tidal characteristics along the eastern Canadian seaboard result from a combination of diurnal (daily) and semidiurnal (twice daily) tides, the latter mostly dominant. Tidal ranges in the upper Bay of Fundy commonly exceed 15 m, in large part a consequence of tectonic forces that initiated the Bay during the Triassic. The existence and position of the Bay is principally determined by a half-graben, the Fundy Basin, which was established at the onset of the opening of the Atlantic Ocean. Due to the proportions of the Bay of Fundy, differences in tidal range through the Gulf of Maine-Bay of Fundy-Georges Bank system are governed by near resonance with the forcing North Atlantic tides. Although Fundy tide curves are sinusoidal, tide prediction calls for consideration of distinct diurnal inequalities. Overlapping of the cycles of spring and perigean tides every 206 days results in an annual progression of 1.5 months in the periods of especially high tides. Depending on the year, these strong tides can occur at all seasons. The strongest Fundy tides occur when the three elements--anomalistic, synodical, and tropical monthly cycles--peak simultaneously. The closest match occurs at intervals of 18.03 years, a cycle known as the Saros. Tidal movements at Herring Cove, in Fundy National Park, illustrate the annual expected tidal variations.
Vigorous quasi-equilibrium conditions characterize interactions between land and sea in macrotidal regions like the Bay of Fundy. Ephemeral on the scale of geologic time, estuaries progressively infill with sediments as relative sea level rises, forcing fringing salt marshes to grow to successively higher levels. Although closely linked to a regime of tides with large amplitude and strong tidal currents, Fundy salt marshes rarely experience overflow. Established about 1.2 m lower than the highest astronomical tide, only very large tides are able to cover the marshes with a significant depth of water. Peak tides arrive in sets at periods of 7 months, 4.53 years, and 18.03 years. For months on end no tidal flooding of the high marshes occurs. Most salt marshes are raised to the level of the average tide of the 18-year cycle. The exact locations of coastal zone water levels such as mean high water and mean low water is a recurring problem and the subject of much litigation.
Marigrams constructed for selected river estuaries illustrate how the estuarine tidal wave is reshaped over its course, to form bores, and varies in its sediment-carrying and erosional capacity as a result of changing water surface gradients. Changing seasons bring about dramatic changes in the character of the estuaries, especially so as ice conditions develop during the second half of the 206-day cycle when the difference in height between Neap tide and Spring tide is increasing, the optimal time for overflow in any season. Maximum ice hazard, including build-up of "ice walls" in Fundy estuaries, occurs one or two months before perigean and spring tides combine to form the largest tide of the cycle. Although "ice walls" and associated phenomena pose hazards for man-made constructions, important natural purposes are served which need to be considered in coastal development and management schemes. Tides play a major role in erosion and in complex interactions among Fundy physical, biological, and chemical processes. Recent observations on mud flat grain size alterations, over deepening areas of the sea bed, and changes in the benthic community indicate changing environmental conditions in the Bay, caused possibly by increased hydrodynamic energy in the system.
Les marees constituent une realite omnipresente dans de nombreuses regions cotieres du monde, et leurs causes et leur influence intriguent depuis longtemps. Il existe peu d'endroits ou les marees jouent un role plus marquant au sein de l'economie et du caractere d'une region et de ses habitats que dans le secteur du rivage de la bale de Fundy, dans l'Est du Canada. La bale de Fundy represente effectivement un merveilleux laboratoire naturel pour l'etude des marees et de leurs effets. Il faut toutefois, pour mieux comprendre ces phenomenes, des perspectives elargies des caracteristiques physiques generales des marees et de leur fonctionnement l'echelle ocdanique. Le passe geologique de la region fournit lui aussi des indices precieux sur la facon dont les marees les plus spectaculaires du globe sont apparues dans la bale de Fundy et sur les raisons de leur presence.
Les caracteristiques des marees le long du littoral de l'Est du Canada decoulent d'une combinaison de marees diurnes (quotidiennes) et semi-diurnes (biquotidiennes), parmi laquelle ces dernieres predominent principalement. Les amplitudes des marees dans la partie superieure de la bale de Fundy depassent communement 1.5 metres, en grande partie en raison des forces tectoniques qui ont sculpte la baie au cours du Trias. L'existence et l'emplacement de la baie sont principalement determines par un semi-graben, le bassin de Fundy, dont l'etablissement remonte au debut de l'ouverture de l'ocean Atlantique. Vu les proportions de la bale de Fundy, les differences d'amplitude des marees a l'interieur du systeme du golfe du Maine, de la bale de Fundy et du Banc Georges sont regies par une quasi-resonance avec les marees de contrainte de l'Atlantique Nord. Meme si les courbes des marees de Fundy sont sinusoidales, les previsions des marees necessitent la consideration d'inegalites diurnes distinctes. Le chevauchement des cycles des marees de vives-eaux et des marees de perigee tousles 206 jours entraine une progression annuelle de 1,5 mois des periodes de marees particulierement elevees. Selon l'annee, ces marees de grande envergure peuvent survenir toutes les saisons. Les marees les plus fortes de Fundy apparaissent lorsque les trois elements--les cycles mensuels anomalistique, synodique et tropique--culminent simultanement. Le jumelage le plus proche survient a des intervalles de 18,3 ans en vertu d'un cycle appele le cycle Saros. Les mouvements des marees de l'anse Herring dans le parc national Fundy illustrent les variations annuelles des marees anticipees.
Les interactions entre la terre et lamer dans les regions macrotidales comme la baie de Fundy sont caracterisees par des conditions de quasi-equilibre intenses. Des estuaires, ephemeres a l'echelle des temps geologiques, se remplissent progressivement de sediments au fur et a mesure que s'eleve le niveau relatif de la mer, ce qui force les marais sales en bordure a passer a des niveaux successivement superieurs. Meme si les marais sales de Fundy sont etroitement lies a un regime de marees de grande amplitude et de courants periodiques puissants, ils debordent rarement. Comme ces marais sont etablis a environ 1,2 metre de moins que les marees astronomiques les plus elevees, seules les tres grandes marees peuvent les recouvrir d'une couche d'eau d'une profondeur substantielle. Les marees les plus importantes se presentent en serie a des periodes de sept mois, 4,53 ans et 18,03 ans. Aucune inondation des marais eleves due aux marees ne survient pendant des mois et des mois. La majorite des marais sales s'elevent au niveau moyen du cycle de 18 ans. Les emplacements exacts des niveaux d'eau des zones cotieres, comme le niveau moyen des hautes-eaux et le niveau moyen des basses-eaux, ne cessent de poser des problemes et font l'objet de beaucoup de litiges.
Les courbes de marees etablies dans le cas de certains estuaires de rivieres illustrent de quelle facon les vagues des marees estuariennes se transforment le long de leur trajet pour former des mascarets et dans quelle mesure varient leur capacite de transport de sediments et capacite d'erosion par suite des variations des pentes de la ligne d'eau. Les saisons qui se succedent entrainent des changements spectaculaires du caractere des estuaires, en particulier lorsque des glaces apparaissent au cours de la seconde moitie du cycle de 206 jours, quand la difference de hauteur entre la maree de mortes-eaux et la maree de vives-eaux s'accroit, moment optimal de debordement au cours de n'importe quelle saison. Le danger maximal de glaces, notamment l'apparition de, << murs de glace >> dans les estuaires de Fundy, survient un ou deux mois avant que les marees de perigee et de vives-eaux se combinent pour former la maree la plus importante du cycle. Meme si les << murs de glace >> et les phenomenes connexes posent des dangers aux constructions erigees, ils servent des fins naturelles importantes qu'il faut considerer dans les programmes d'amenagement et de mise en valeur des cotes. Les marees jouent un role marquant dans l'erosion et dans les interactions complexes au sein des processus physiques, biologiques et chimiques de Fundy. Les observations recentes des modifications des grosseurs des grains des vasieres, les secteurs d'approfondissement marque du plancher oceanique et les changements survenus dans la communaute benthique revelent que les conditions du milieu de la baie changent, possiblement en raison de l'energie hydrodynamique accrue q l'interieur du systeme.
[Traduit par la redaction]
1. Wave and Tide Fundamentals
Oceans cover nearly three quarters of planet Earth. Our lives are intimately linked to them and to their tides in diverse ways, most of which we poorly appreciate. Subject to fanciful theories and speculations for thousands of years, tides have long piqued our curiosity. Sir Isaac Newton (1642-1727) first identified gravitational forces as the prime movers in tide generation. He laid the basis of tidal theory, conceiving an "equilibrium tide" that would apply to ideal conditions of a global ocean. Pierre Simon de Laplace (1749-1827) shares honours with Newton because he formulated equations of motion for tides on a rotating Earth, and was first to distinguish tidal phenomena according to different types (species) of tides. Laplace perceived the harmonic method of analyzing tides, later elaborated by Lord Kelvin (1824-1907), inventor of the earliest tide-predicting machine in 1872.
Yet despite the ease with which tide tables are now constructed, no one to this day really comprehends how gravitational forces work. Neither has anyone been able to conceive a purely dynamic theory to directly relate tide-generating forces to actual tides (Clancy 1969; LeBlond and Mysak 1978). Laplace recognized that there could be no perfect theory, the chief difficulty being Earth's rotation. He preferred to write in terms of tidal waves, with the same periods as those induced by rhythmical components of gravitational forces. The problem of tides is that of a fluid motion modified by the geometry (including depth) of ocean basins, by friction, and by such forces as the Coriolis effect due to Earth's rotation.
The ebb and flow of tides provide fascinating measures of an ocean's pulse (Defant 1958). Nowhere does this beat more impressively than in the Bay of Fundy on the western shore of the North Atlantic Ocean. Here the tide attains world record levels, with tidal range approaching 16 m at times of particular astronomical conditions. Storm surges, tidal bores that gain height in an estuary, and great waves that batter the shore: all stir the blood and instil respect for the raw power of nature.
Other processes related to tides, among them currents, shifting sediments, erosion, development of tidal estuaries, and salt marsh growth and decay, work more subtly, creating changes over decades, centuries and millennia, rather than in a matter of hours or days. These processes, in turn, evolve in response to postglacial sea-level recovery. The unmistakable hand of Homo sapiens too, is now everywhere evident along the shore, for it is in the world's coastal zones that humankind has by choice become most concentrated.
The main purpose of this review is to provide a general survey of tides and an overview of their relationship to, and effect on, the Bay of Fundy (henceforth sometimes referred to as "the Bay"), home to the world's highest tides. Worldwide there is now an increased focus on understanding tidal processes and documenting changes on short-, medium-, and long-term time scales by various historical and scientific means. The Bay of Fundy and its tidal processes form a dynamic entity, and serve as a model for comparison with similar tidal regimes elsewhere.
1.2. WAVES AND WATER PARTICLES
1.2.1. Water waves: vibrations subject to gravity
Long before Aristotle (384-322 B.C.E.) wrote about the relationship between wind and waves, mankind had been engaged in the study of waves. Yet despite the writings of Aristotle, Newton, Kelvin, Stokes, Helmholtz, and others, details of the physics of wave oscillations are still being worked out. Here we no more than touch on this vast subject. Splendid comprehensive elementary treatment of waves--tidal and otherwise--is provided by Pethick (1984), Pugh (1987) and Sverdrup et al. (2003).
Waves in general play an important role in meteorological and oceanographic processes such as mixing in the upper ocean layer and production of oscillatory currents, as well as a number of processes involving air-water interactions. Ocean waters do not conform precisely to the dynamics of idealized fluids upon which mathematical models of wave behaviour are based. Even so, a water wave is essentially a vibration subject to gravity. With this in mind we briefly examine the birth of waves in water and the characteristic oscillatory behaviour required to produce ordinary tide waves (or "tidal waves", not to be confused with the improper popular synonym for tsunami).
In any material at rest, except of course for vibrations on an atomic scale, none of the particles of the material are moving in relation to each other. However when an external force moves some of the particles out of their rest positions without breaking a bond, tension is built up within the material. If the external force is relaxed, the displaced particles will return toward their former positions: to do so they have to move with a certain velocity thus giving them momentum. However, this momentum will not immediately disappear when the particles reach their rest positions. They will overshoot, building up a new tension in reversed direction. The particles will continue to oscillate about their rest positions, their displacement dependent upon the strength of the initial force. Because the moving particles come into contact with other particles that do not move in the same direction or at the same rate, the energy that started the oscillation will eventually be dissipated over more and more smaller, sub-atomic particles, increasing the temperature of the material.
At Earth's surface, gravity compels all particles making up a body of water to be collectively drawn as close to the centre of the Earth as the container will allow. Hence, the surface area of a small body of water is virtually a flat plane, with all points on it being the same distance from the centre of the Earth. Disturbances from external sources of energy cause some of these particles to move horizontally. The result is that some particles are raised to an elevation higher than the rest plane, leaving a void where they have been removed. When external energy sources are removed, higher particles will tend to move back towards the void, creating an oscillating motion. Another factor that needs to be considered is surface tension. Water particles have an affinity for each other, and when this linkage is disturbed, surface tension will tend to restore the displaced particles to their original positions. However surface tension is a much smaller force than that of gravity, especially if large masses are involved, and it is only important when the displacements are small.
When displacement occurs, more water particles per unit area are above a certain datum plane in a given area than there are at nearby unit areas. (Since water is about as compressible as high strength steel, this means that the water level in the area where the particles are moved is higher than the original rest plane.) In this highly simplified wave, the place where the water is at the highest level is called the crest and that of the lowest level is called the trough.
To illustrate some further basic concepts, imagine a stone thrown into water: the stone's impact causes a set of concentric ripples to move outward. The distance between the crests of two subsequent ripples is called the wave length, L. The time it takes for a wave to move over the distance of one wave length is called a period or cycle, T. The vertical distance between the crest (High Water) and the trough (Low Water) is the height, or range of the wave. Half the range is called the amplitude A, and represents the maximum displacement of the wave from the rest plane. The frequency, f, is the number of cycles that pass a given location during a unit of time. The most common period of a tidal wave is 12.42 hours; thus its frequency (the reciprocal of the period) is 0.08051 cycles per hour. The ware speed or celerity, c, is the horizontal rate of advance of the wave as a whole, where c = L/t = f * L (see Fig. 1.).
[FIGURE 1 OMITTED]
1.2.2. Wave forms and wave types
The form of a water wave is most commonly like a sine or cosine curve. As the crest of a wave is its most visible feature, it is customary to express the shape of a wave as a function of time t:
(1) [H.sub.t] = A * cos(360 * f * t) or, A * cos(2[pi] * f * t) = A * cos(n * t)
where t is the time from the original High Water occurrence, at the location where High Water occurs at t = 0. It can also be expressed as a function of the location at the distance x:
(2) [H.sub.x] = A * cos (360 * x/L) = A * cos(2[pi] * x/L) = A * cos(k * x)
where k is the wave number, and x is the distance from the location where High Water occurs at that point in time. The angular speed, n, of a wave is equal to 360. f when the angle is measured in degrees, and equal to 2[pi] * f when measured in radians, as is used in (1). The wave number, k, is equal to either 360/L or 2[pi]/L, depending on whether degrees or radians are used, as in (2). Although (1) and (2) are the most convenient ways to express the shape of a wave, it is not always possible to use them. A more general equation is required if one wishes to use time in a particular time zone, or the time that the actual or alleged cause of the wave occurs, or when one wants to compare or combine one wave with another (Eagleson and Dean 1966). This equation can be written as follows:
(3) [H.sub.u](x,t) = A * cos(2[pi](t/T-x/L)), or
(4) [H.sub.u](x,t) = A * cos(n * t - k *x)
These equations describe a progressive wave moving in a positive x-direction at the distance x in time t. When the argument (n * t - k * x) is equal to zero, High Water will occur. This means that High Water will occur when t = T * x/L = k * x/n.
When the wave moves in the opposite (negative) x-direction, the appropriate equation becomes:
(5) [H.sub.d](x,t) = A * cos(n * t + k * x)
When two waves with the same amplitude A, and the same frequency for period T, are moving in opposite directions, the resultant wave will be a standing wave which can be described by the following equation:
(6) [H.sub.s](x,t) = [H.sub.u] + [H.sub.d] = A [cos(n * t - k * x) - cos(n * t + k * x)] = 2A * cos(2[pi] * t/T) * cos(2[pi] * x/L)
Figure 2 illustrates the consequences of such an event. [H.sub.s] is maximum when t = 0, or t = T and x = 0, or x = L or when t = 0.5T and x = 0.5L. [H.sub.s] is minimum when t = 0.5T and x = 0 or x = L (or when t = 0, T and x = 0.5L). [H.sub.s] is 0 at all places when t = 0.25T or t = 0.75T or at all times when x = 0.25L or x = 0.75L (node). Note that at any value oft the shape of the wave will be that of a cosine curve. At the closed end of a channel, should a progressive wave be reflected, a standing wave may form. Thereby the energy of the wave is temporarily transformed into potential energy. In theory wave height can double as indicated by the factor 2A in (6). The maximum vertical fluctuations occur at the end of the channel and at locations that are distant from the end by multiples of half the wave length. These locations are called "anti-nodes", whereas at the "nodes" halfway between there will be no surface fluctuations. However, strong currents will be in evidence because the water flows to and fro between the anti-nodes. Consequently, when the water surface is high at the "even" anti-nodes, it will be low at the "odd" anti-nodes.
[FIGURE 2 OMITTED]
In the foregoing discussion, it is assumed that the wave height is small relative to wavelength and water depth. Although the range of the wave will always be small relative to wave length, it need not be so with respect to the depth. As derived from the dispersion relation, the wave speed of a sinusoidal wave in a body of water can be expressed as:
(7) c = [[(g/K)tanh(K x D)].sup.0.5]
where D is water depth, g is acceleration due to gravity, and K is wave number 2[pi]/L. If the relationship between depth D and wave length L is expressed as L = m x D, one can calculate the wave speed for different values of the ratio m. When m is small, wave speed, c, tends towards the value of [(g/K).sup.0.5]; when large, it will approach [(g x D).sup.0.5]. In the first situation, the waves are termed deep water waves, and in the latter case shallow water waves (see Table 1).
In the Atlantic ocean, where water depths are in the order of 5000 metres and both the distance across and the tidal wave length, L, are about 5000 km, the value of m is approximately 1000. Thus, even oceanic tidal waves are shallow water waves, affected by ocean depth. Particle motions in shallow waves are uniform with depth. Since water depth affects celerity or wave speed, waves moving into shallower water will decelerate. If, at the right flank of the wave, water is shallower than on the left flank, the wave on the right side will fall behind the wave crest on the left side. In effect, wave crests tend to conform to the depth contours over which they are moving. Thus, a wave approaching an island that rises very steeply from the ocean bottom, will pass the island unchanged, whereas a wave approaching an island surrounded with a gradually shallowing shelf tends to move toward the shore line in nearly concentric circles. This bending of the wave crest because of changing depths is called refraction.
There is a relationship between the wave speed, c, and the speed of the particles in the oscillating body of water. The particle displacement amplitude, u', can be expressed as follows:
(8) u' = (A/D) x c
where A is the amplitude of the tidal wave. For shallow water waves, this equation becomes:
(9) u' - [A(g/D).sup.0.5]
This means that the amplitude of the particle movement becomes:
u = T x u'/(2[pi])
The relationship between period and wave length in this situation is expressed as:
(10) L = c x T
where T is the period of the wave. The period of the most common tidal movement is 12.42 hours or 44 714 seconds. In the Atlantic, the tides have an amplitude of approximately 0.45 m. Table 2 provides the characteristics of a tidal wave of these dimensions in waters of various depths.
Note that in waters 5000 m deep, particle displacement from its rest position needs to be only 142 m during a tidal period in order to make a tidal wave possible. For shallower water on the continental shelf, the required displacement becomes thousands of metres. The gravitational influences of the Moon and the Sun countering those of the Earth cause these particles to move. In contrast to wind movements, which only create a shear force at the surface of the water body, these gravitational influences act on particles at all depths of the ocean.
We turn next to the generation of shallow-water waves in the oceans.
1.3. TIDES AND TIDE GENERATION
Tides, the longest of oceanic waves, involve alternating rise and fall of sea level due to gravitational effects exerted on the Earth by the Moon and Sun. People have long recognized that there is a connection between tides and the positions of the Moon and Sun relative to Earth. However, the nature of this connection is by no means obvious, and the influence of these celestial bodies on tidal events results in complex flow patterns. Nevertheless, the magnitude of the effects that generate tides can be precisely calculated from the astronomy alone, the chief caveat being that the ocean's response to these effects will be constrained by continental landmasses, the Earth's rotation, the geometry of ocean basins, and the transience of weather. According to Newton's equilibrium tidal theory, an ideal wave forms instantaneously upon an Earth uniformly covered by a deep layer of water, under the influence of the gravitational effects of the Moon and Sun. This theory is not meant to provide a realistic picture of what actually occurs in nature, but it does give accurately the tidal periods, the relative forcing magnitudes, and the astronomical phases of the tides. It is this idealized calculation that forms the cornerstone upon which tidal analysis and predictions are based.
The dynamic tidal theory employed by oceanographers shows that there is no wave crest formed instantaneously in the ocean directly under the Moon (or Sun), or at its antipodal point. The vertical tide movements at most locations can be represented by a time-space graph in the form of a modified sinusoidal curve like that of a simple harmonic motion. In harmonic motion, an object is accelerated by a variable force, the strength of which can be represented by a sine curve. Half the time this force will have a positive direction. When this force becomes zero at the moment it changes to a negative direction, the resulting velocity will reach its maximum strength. The velocity graph throughout the cycle will also be sinusoidal, but 90[degrees] out of phase with acceleration. The object moved by the force will reach its farthest displacement in the positive direction when velocity becomes zero. This means that instead of a "tidal bulge" as customarily shown to be formed beneath the Moon, there will be a depression. Thus, generally only horizontal or "tractive" forces are responsible for generating tidal movements in the ocean.
It is important to note here the three main astronomical reasons for variations in the strength of these gravitational forces:
1. Variable distance between Moon and Earth. This variation causes the greatest deviations from the average (mean) tide in the Bay of Fundy. Because the Moon's orbit is elliptical, once a month at perigee the Moon is closest to the Earth, and thus its gravitational pull is then at its greatest, resulting in stronger than average tides. These so-called perigean tides recur every anomalistic month of 27.555 days.
2. Variable celestial positions of the Moon, Sun, and Earth relative to each other. The cycle of the Moon's phases in which there are two sets each of spring and neap tides, is the synodical month of 29.531 days. In the first set, spring tides are stronger than average because the Earth is either between the Sun and Moon (full moon), or the Moon is between Earth and Sun (new moon). A week later, during the first or last quarter of the moon, its gravitational influence is diminished by that of the Sun, which is then acting at right angles. The resulting tides, weaker than usual, are called neap tides.
3. Declination of the Moon and Sun relative to the Earth's equator. Declination is the angular distance in degrees between a heavenly body and the celestial equator (the plane in which the Earth's equator is situated) when it passes through the local meridian. A complete cycle, in which the Moon crosses the Equator twice, lasts 27.322 days and is called a tropical month. However, it takes 18.6 years for the Moon to complete its cycle of maximum declination, ranging between 28.5[degrees]N and 28.5[degrees]S with reference to Earth's equatorial plane.
One can expect stronger than usual tides a few days later than full and new moon, and weaker tides near the quarter phases of the moon. There is a certain inertia in the development of the tides, analogous to the fact that the months of July and August are on average warmer in the Northern Hemisphere than June, when the days are longer and the Sun is higher. For this reason the highest tides occur a few days after the astronomical configurations which induce them.
1.3.2. Tidal prediction
Tidal predictions are based on harmonic analysis of local tides. In the Bay of Fundy (Fig. 3) the principal hydrographic station is located at Saint John, New Brunswick. [Henceforth, New Brunswick will be abbreviated to N.B. and Nova Scotia to N.S.] Predictions are made and published annually for this reference port. Upon analysis, the observed tides are broken down into a large number of cosine curves, so-called tidal constituents, each representing the influence of a particular tidal influence or characteristic of the local tide. The first seven harmonic constituents listed in Table 3 account for >90% of the total variability of the tides. As many as 62 tidal constituents are routinely used for tide prediction. The [M.sub.2] constituent represents the influence that the Moon has on the local tides, supposing for simplicity that it makes a circular orbit around the Earth in the plane of its equator at a distance resulting in (most cases) average tides. The [S.sub.2] constituent represents the Sun's gravitational influence, assuming that Earth moves in a circular orbit around the Sun at a distance producing the average effect, and assuming that the Earth's equator is located in the ecliptic. Other constituents make corrections to these basic assumptions, because of variations in actual and sometimes apparent movements of these heavenly bodies. Constituents with the subscript "2" repeat themselves twice a day, causing two daily (semidiurnal) tides. Those with subscript "1" occur once a day, and those with subscript "4", four times a day. The [K.sub.4] constituent is the main overtide in the Bay of Fundy. It appears where the usual sinusoidal shape of the tidal wave is distorted upon entering shallow, narrowing inlets. This process results in loss of symmetry of the tidal wave, causing the water to rise faster than it will drop in the following ebb (Forester 1983; Canadian Hydrographic Service 1981).
[FIGURE 3 OMITTED]
Nowhere does the pulsating ebb and flow of the tide beat more impressively than in the Bay of Fundy (Defant 1958). Here the tidal range exceeds 16 m at times of particular astronomical conditions. Fundy tides are an integral part of the semidiurnal tidal system prevailing in the North Atlantic area (Davis and Browne 1996).
1.3.3. The tide-producing forces
In Atlantic Canada there are usually two unequal tides each day. They are due to the combined gravitational effects of the Moon and Sun, and the centrifugal forces resulting from the revolution of the Earth-Moon and Earth-Sun systems around their common centres of gravity. For instance, the Earth and the Moon revolve in essentially circular orbits round their combined centre of mass (barycentre) every 27.3 days (sidereal month). Thus every point on Earth has an angular velocity of 2[pi] per 27.3 days, and each will experience an equal acceleration as a centrifugal force away from the Moon. The total of all these forces on the mass of the Earth is balanced by the total gravitational effects of the Moon's mass on Earth's mass, keeping the Earth on its orbit, just as the gravitational effects of the Earth keep the Moon on its orbit (Doodson and Warburg 1941; OPEN 1993). The magnitude of the force ([F.sub.g]) keeping these bodies on their respective orbits can be expressed with the following equation:
(11) [F.sub.g] = G x [M.sub.e] x [M.sub.m]/[R.sup.2]
where [M.sub.e] and [M.sub.m] are the masses of the Earth and Moon, G the universal gravitational constant, and R the distance between the centres of [M.sub.e] and [M.sub.m]. Further, the Moon's gravitational attraction on all particles making up the Earth is directed towards the centre of the Moon and hence, except for the line joining the centres of the masses of the Earth and Moon, will not be exactly parallel to the direction of the centrifugal force. The composite magnitude of the centrifugal and gravitational effects, known as the tide-producing force ([F.sub.TP]) will depend on the distance of each particle of Earth from the centre of the Moon. This distance can be more or less than the value of R.
The magnitude of [F.sup.TP] (Fig. 4) on a particle with the mass m at point Q, in relation to a similar particle at the centre of the Earth, for example (given the Earth's radius = a), is:
(12) [F.sub.TP] = G x [M.sub.m] x m/[(R-a).sup.2] - G x [M.sub.m] x m/[R.sup.2]
[FIGURE 4 OMITTED]
In this equation the last part represents the equivalent centrifugal effect. The equation is simplified by means of a calculus derivative to:
(13) [F.sub.TP] = 2 x G x [M.sub.m] x m x a/[R.sup.3]
At point Q (Fig. 4) the [F.sub.TP] acts toward the Moon (a is positive), but at point P, away from it (a is negative). At these points the effect is perpendicular to the Earth's surface and, although at its maximum value in relation to the Earth's gravity, it is insignificant and has negligible effect on raising the water surface. The [F.sub.TP], will be zero in the plane through the centre of the Earth perpendicular to the line connecting it with the centre of the Moon. However, at points on the Earth's surface halfway between this plane and points Q and P (W, X, Y and Z), the horizontal components (tractive forces) of the [F.sub.TP] will be greatest, causing maximum effects and moving particles towards points Q and P (Clancy 1969).
These forces will cause particles in the oceans to move along looping paths of limited distances, but enough to cause the tidal movements. The looping patterns are thus variable for each latitude, season, and phase of the Moon--see Desplanque and Mossman (1998a) for charts of particle movements. For example, during its new--and full-moon phases, the Moon makes its transit through the local meridian at 12:00 and 24:00 hours, and during its first and last quarter phases at 06:00 and 18:00 hours. Individual water particles reach their most westerly displacement position during the evening in the summer, and during the morning in the winter and, whereas the tides in the ocean are chiefly semidiurnal, the looping tracks of the individual particles are mainly diurnal. The ocean water would thus receive an impulse with every second oscillation, in contrast to the pendulum of a grandfather clock that, through its escapement wheel, receives an impulse every oscillation. The dimensions of the loops indicate that the movement of the water particles can maintain the tidal movement in deeper waters, but not in shallow ones. The movements, in sum constituting a progressive tidal wave, measure in mid-ocean a few hundred metres at most. However, like water spilled from the edge of a shallow dish, tidal effects become more evident in shallowing coastal waters where rotary tidal currents of amphidromic systems are impeded.
1.3.4. Variations in strength of the tides
18.104.22.168. Gravitational influences and accelerations.
On average, the Earth requires 24 hours to revolve with respect to the Sun. Similarly the Moon seems to travel around the Earth in 24 lunar hours, equivalent to 24.84 solar hours. To illustrate the different possible situations, the Sun is used in the following discussion; the Moon could also be used, but the periods would then be measured in lunar hours.
First, consider the Sun's gravitational influences on a particle of water subject to semidiurnal oscillations near the Equator. At sunrise, around 06:00 hours, the particle is on (terminator) circle T. It is not accelerated horizontally (Fig. 5). However, shortly afterwards it will be drawn toward the east, to be accelerated strongest in that direction at 09:00 hours. The acceleration ceases at noon, to be replaced shortly afterwards by a westerly acceleration, which will be at its maximum at 15:00 hours. At 18:00 hours this acceleration will be reversed to an easterly acceleration. The process is repeated over and over again in cycles of 12 solar hours. When the acceleration in an easterly direction stops at 12:00 hours and at 24:00 hours, the particle affected by it will reach its maximum velocity in this direction. The maximum velocity in a westerly direction will occur at 06:00 and 18:00 hours (Fig. 5). The particle will not move at 03:00, 09:00, 15:00 and 21:00 hours. Note that when the particle is accelerated the fastest to the east, it is at its most westerly position in its semidiurnal oscillation.
[FIGURE 5 OMITTED]
If the vertical accelerations caused by the Sun and Moon were of any consequence, the same reasoning could be used. In the case of the Sun these accelerations would be strongest upward at noon and midnight, and strongest downward at 06:00 and 18:00 hours. This means that the displacement of the water surface (Fig. 5) would be downward at noon and midnight.
Because the horizontal or tractive accelerations need not compete with much stronger terrestrial gravitation, they can set water particles in motion in the almost frictionless ocean because neighbouring particles are subject to almost identical influences. A constant acceleration of 8.4 x [10.sup.8] x g (8.237 x [10.sup.-7] [ms.sup.-2], applied for one hour to a particle originally at rest, will impart to that particle a speed of 0.003 [ms.sup.-1], or 10.8 m/hr. The distance travelled in that interval is 5.4 m. In a three hour period, the velocity will have been 24.4 m/hr and the distance travelled 48.6 m.
22.214.171.124. The distance factor.
Once in the anomalistic month of 27.555 days, the Moon's distance from Earth is 92.7% of the mean distance between the two bodies. Since the effect of the Moon's gravitation on the particles in the ocean is inversely proportional to the cube of the distance, the effect is 1.255 times stronger than the average effect. Approximately 14 days later, with the Moon in apogee, the distance is 1.058 times the average distance and the Moon's effect is reduced to 84.4% of its average value. The Earth is closest to the Sun shortly after New Year, making its influence 5.2% stronger than average, while in the first days of July its effect is reduced by 4.9%. Thus, in theory, the Moon's effect varies between 0.844 and 1.255 times its average effect because of varying distance, while for the same reason the Sun's effect varies between 0.438 and 0.484 times the Moon's average effect.
126.96.36.199. Springs and neaps.
The relationship between synodical month and the mean semidiurnal reappearance of the tide "[M.sub.2]" is given by [M.sub.2] = 12 (1-1/M) = 12.42 hours (12 hours and 25 minutes). Twice during the synodical month, the Earth, Moon, and Sun are almost aligned. The gravitational effects of Sun and Moon are additive and the so-called spring tides are stronger than usual. Due to inertia in the development of tides, the highest tides occur a few days after the appropriate astronomical configurations. Such tides are called spring tides because they spring or reach higher than normal. When the tides along the European coastlines are analyzed it turns out that the actual effect of the Sun is between 0.3 and 0.4 times that of the Moon's effect, a little less than the theoretical value of 0.46. Thus, the bimonthly variation in this region is between 0.6 and 1.4 times the mean tide, more than caused by the variation in the distance between Earth and Moon. Small wonder, therefore, that western Europeans have regarded the cycle associated with changing Moon phases as the most important one. When the Moon is in either the first or last quarter, the actions of the Moon and Sun are perpendicular to each other and tend to counteract each other. Because the Moon's effect is the strongest, it will prevail, but in a reduced fashion. When this condition exists, the tides are called neap tides, a Saxon term related to the Germanic word "knippen", to pinch, meaning that they are reduced in size. In waters bordering most of North America, the influence of the Sun on the tides is itself rather "nipped". Consequently, the tidal variations caused by once-monthly so-called perigean tides are much more prominent.
188.8.131.52. Diurnal inequality.
Tides are generally semidiurnal, i.e., there are two High Waters and two Low Waters during a day, be it a solar or a lunar day. The strength of tides is modified by changing distances between Earth and Moon, and between Earth and Sun, and also because the Moon and the Sun act from varying directions. Changing declinations of the Sun and the Moon with respect to the plane of the ecliptic cause diurnal variations in the strength of the tides, a phenomenon called diurnal inequality. Usually, both the two High Waters and the two Low Waters during a day are affected, their respective levels being unequal. Elsewhere, High Waters during a day reach almost equal levels, in contrast to the levels of the Low Waters, which may be different.
The declination of the Sun is due to the fact that the plane of the Earth's equator makes an angle of 23.452[degrees] with the plane in which the Earth orbits the Sun (Fig. 6). Hence the Sun appears higher in the sky during summer in the Northern Hemisphere, reaching its highest point at noon on 21 June. Conversely, at noon on 21 December the Sun appears 46.9[degrees] lower above the horizon. Thus, summer days are longer than summer nights, and winter days are shorter than winter nights. At an equinox, the Sun is overhead at the Equator on about 21 March and 23 September, the day length is the same as night length everywhere on Earth. The Sun is said to have a north declination between the spring and fall equinoxes, and a south declination during the remainder of the year.
[FIGURE 6 OMITTED]
The Moon goes through a similar but much shorter declinational cycle, lasting 27.322 days. As the Moon's plane makes an angle of 5.145[degrees] with the ecliptic, the declination of the Moon is more variable than that of the Sun. Thus, there are years when the declination of the Moon ranges from 28.597[degrees] North to 28.597[degrees] South, 14 days later. This condition existed in 1987 and will occur again in 2005, 18.6 years later. But in 1996 the maximum variation in declination of the Moon ranged between 18.307[degrees] North and South.
The declinations of the Moon and Sun have a great influence on the directions of the accelerations affecting particles in the oceans. During an equinox, not only days and nights are of equal duration, but the two tides caused by the Sun will also have the same strength. Nor is the Moon able to produce diurnal inequality when it crosses the plane of the Earth's equator. Because the Moon's orbit is never more than 5[degrees] from the ecliptic, the Moon's declination is close to the Sun's declination when there is a new moon. At full moon, it has an opposite declination to that of the Sun. Consequently, the only periods during which both Sun and Moon can cause little or no diurnal inequality are when there is a full or new moon near an equinox. These two periods fall annually between 8 March and 3 April, and between 10 September and 6 October. For the remainder of the year either the Moon or the Sun, or both, will be in declination. The role of diurnal inequalities in the Bay of Fundy is explored in greater detail in a later section (8.3.3).
1.4. THE CORIOLIS EFFECT
As a result of Earth's rotation, any object freely moving near or in contact with its surface will veer to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is called the Coriolis effect. It affects winds everywhere, and in the oceans it results in the circular motion of water. The French mathematician Gaspard Gustave de Coriolis explained the phenomenon, applicable to frictionless motion, early in the 1800s. The effect is caused by Earth's eastward rotation. At the Equator the eastward movement of the planet's surface is about 1670 km/hr (actually, 6378.16 km x [pi] x 2/24 = 1669.8 km/hr), but falls off at higher latitudes as the circumference of the Earth, in the axial plane normal to Earth's axis, gradually decreases (OPEN 1993). Thus at 45[degrees] latitude the velocity is about 1200 km/hr (1179 km/hr), falling off to zero at the poles. Any object freely moving away from the Equator, north or south, is moved to the east at higher latitudes because of higher eastward inertia. Conversely, an object approaching the Equator from north or south is effectively retarded due to smaller eastward inertia; it is moved to the west as it approaches the Equator from either north or south. Consequently, essentially frictionless objects such as wind and ocean currents, and tidal waters entering and leaving coastal embayments, are deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
In the case of the atmosphere, air moves from high pressure areas to depressions. The depressions are filled from all sides, and air currents are deflected to the right by the Coriolis effect. However, the result is that the winds approaching and converging near the depression, in the Northern Hemisphere, form a cyclonic anticlockwise circulation. Water surfaces beneath a developing atmospheric depression, rise in elevation, drawing water from areas under high pressure systems. Famous whirlpools, such as the Maelstrom off Norway, and the Old Sow near Deer Island in Passamaquoddy Bay in the Bay of Fundy, are also subject to the Coriolis effect.
Flat rotating objects such as a record player or merry-go-round can be used to illustrate the Coriolis effect. In terms of vector algebra, the fundamental relations are briefly set out below; they apply to the apparent centrifugal force working on a particle in a circular orbit and its counterpart, the centripetal force, which keeps it on this orbit.
1.4.2. Fundamental relationships
In relation to the stars, the Earth rotates once in a so-called sidereal day, which lasts 86186 seconds. Thus each particle in or on Earth has an angular velocity of w = 2 [pi]/86186 = 7.29 x [10.sup.-5] radians per second. Its linear velocity depends on its distance from the Earth's axis, which runs from pole to pole (Doodson and Warburg 1941).
Now consider an object of mass m, moving along the circular path (Fig. 7a) with a velocity V. If it takes t seconds to go around the circle at a constant speed, the object's velocity will be V = 2 [pi] x R/t, in which case the angular speed is w radians per second (w = 2[pi]/t). Thus, the linear velocity V = w x R. If this mass moves from point A to point B on its circular path, it is deflected the distance DB (= x) from the straight path it would have taken had it not been constrained by some force. If the distance AB was covered in t seconds, the force f must have been 2x/[t.sup.2] [ms.sup.-2], because
(14) x = 0.5 f x [t.sup.2].
[FIGURE 7 OMITTED]
When the angle w is very small, AD is approximately the same as AB and is equal to V x t and w x R x t (Fig. 7b), whence:
x = R - R cos w x t = R(1 - cos (w x t)),
1 - x/R = cos (w x t) = [(1 - [sin.sup.2] (w x t)).sup.0.5], [(1 - x/R).sup.2] = 1 - [sin.sup.2] (w x t),
1 - 2x/R + [(x/R).sup.2] = 1 - [sin.sup.2] (w x t).
Now, [(x/R).sup.2] is insignificantly small, and when w x t is small, [sin.sup.2] (w x t) = [(w x t).sup.2], because w is measured in radians. Thus, 2x/R [approximately equal to] [(w x t).sup.2], and x [approximately equal to] R [(w x t).sup.2]/2. Since x is the distance a mass is moved by force f, in t seconds, 0.5 R x [(w x t).sup.2] [approximately equal to] 0.5 f x [t.sup.2], and,
(15) f [approximately equal to] R x [w.sup.2] [approximately equal to] [V.sup.2]/r, (since V = w x R)
Thus the apparent centrifugal force acting on mass m is m x [V.sup.2]/R. Taking w as the angular velocity, then V = R x w, and the centrifugal force, may be expressed as m x R x [w.sup.2] (Fig. 7c).
Suppose now that a particle with mass m, is moving along a circle with radius R, at latitude l. Its velocity is R x w, and the centrifugal force acting upon it will be m x R x [w.sup.2]. Relative to the Earth, it seems to be at rest. However, if it is given a velocity V in the direction of rotation, its real velocity in space will be R x w +V, or R(w + V/R), its angular velocity having been changed from w to (w + V/R), and the apparent centrifugal force acting upon it m x R [(w + V/R).sup.2], which is equivalent to:
(16) m x R x [w.sup.2] + 2m x w x V + m x [V.sup.2]/R
The first term in (16) is the normal centrifugal force resulting in the equatorial bulge, and is balanced by the slope from Equator to the poles of the Earth. The third term is very small because of the divisor R, and can be ignored. The remaining middle term can be split into vertical and horizontal components (Fig. 7d). The vertical one will affect the local apparent gravity force, but the horizontal component will cause a tractive force acting along the Earth's surface, effectively moving the mass to the right (in this case toward the Equator, the initial motion having been west to east in the Northern Hemisphere). The magnitude of this Coriolis effect is 2m x V x w x sin l. In general, the coefficient of this force, acting on a mass m, moving relative to the Earth's surface with a velocity V, is expressed as:
(17) f = 2V x w x sin l
Centrifugal force, unlike gravity, is affected by the relative speed of the object. Thus even an object traveling due east (Northern Hemisphere) undergoes an apparent deflection. This is because it has an angular rotational velocity (measured in degrees or radians/unit time) exceeding that of Earth's surface. The result of this imbalance causes the object to deviate to the right, towards the Equator, away from Earth's axis of rotation. The principle applies to any freely moving object provided it is not on the Equator no matter what its direction with respect to our rotating frame of reference.
The Coriolis acceleration thus expressed is proportional to the speed of the moving object and its latitudinal position. The magnitude of this "force" increases with increasing latitude, and the speed of the moving object, and is dependent upon the rotational velocity of Earth on its axis (Tolmazin 1985). Only at the Equator, where sin 1 = 0, is there no Coriolis effect. Nevertheless it is important to appreciate that Coriolis deflections are not real. They are apparent deflections resulting from observations made at a fixed location to track freely moving objects.
1.4.3. Applications to tides and water currents
Frictional coupling between moving water and Earth is weak except for a thin layer directly adjacent to the solid Earth. Consequently lateral water movements induced by tide generating forces respond readily to the Coriolis effect to an extent that is directly proportional to the mass and the speed of the object in question. Thus, one litre of water, having a mass of 1 kg, and moving at a speed of 1 [ms.sup.-1] (1.944 knot) in relation to the Earth at 45[degrees]N latitude, will be moved to the right of its original direction. It will have been deflected by the Coriolis effect with an acceleration of:
4 x [pi]/86186 x sin 45[degrees] = 1.031 x [10.sup.-4] [ms.sup.-2]
(as the angular velocity = 2[pi]/86186 radians/s). This is about 95 112 times smaller than the Earth's gravitational force. To compensate for this deflective force, a rising slope to the right of 1:95 112 would be caused by the Coriolis effect in the Northern Hemisphere. The slope of this gradient is given by the ratio 1:g/ (2 x V x w x sin l). For example, if a channel has a surface width of W metres, and is carrying a current of C [ms.sup.-1] or of K knots, the water flowing at the right bank will be H m higher than on the left bank. The amount H can be established by
(18) H = W x C/67254 x sin l
(where 67245 = 9.80/4[pi] x 86186 [ms.sup.-1]) or,
H = W x K/130733 x sin l
(where 130732 = 9.80/4[pi] x 67254 x 1.944 [ms.sup.-1], for conversion from knots). In the above two cases, the dimensions are given respectively as follows:
Dimensions: W m, C [ms.sup.-1], whence H = [m.sup.2]s/m/s = m
Dimensions: W m, k = 1852 m/hr = 0.5144 [ms.sup.-1] = 1 knot
In the Bay of Fundy and elsewhere, tidal ranges in wide stretches of water with strong tidal currents will be higher on the side of the channel that is to the right of the flood tide. When the tide reaches its peak level at any segment of the tidal estuary or channel, except for the uppermost reach of the tide, the water continues flowing landward because waters in the upper reaches will still not have reached their maximum level. Some time is required before the tidal current in the upper reaches comes to a standstill and then reverses. When the highest level is reached, the incoming tide will be higher at the right bank than at the left bank. Thereafter the water will be at a lower level and falling. In some instances the ebb current may be faster than the inward flow, causing a steeper lateral slope, but at a lower level. However the incoming tide will be more concentrated at the right bank. In the Bay of Fundy this will be at the southern or Nova Scotia side of the Bay, while the outgoing tide will be higher at the northern or New Brunswick side, resulting in an anticlockwise movement of the bulk of the tidal water.
Charts of the Bay of Fundy indicate that near Saint John, N.B., the Bay is 57 km wide. Tidal currents in that region have an average incoming velocity of 1.7 knots or 0.875 [ms.sup.-1]. Under these conditions the lateral water surface gradient due to the Coriolis effect can be calculated from equation (18) as:
H = 57000 x 0.875 x sin 45[degrees]/67254 = 0.52 m (or H = 57000 x 1.7 x sin 45[degrees]/130732 = 0.52 m).
That is to say the water level on the Nova Scotia side is 0.52 m higher than on the New Brunswick side. This will be higher during the periods of maximum velocity, and lower when the velocities are lower than average.
At High Water in Saint John, the water continues to move towards the head of the Bay, where High Water occurs some time later. Assuming the current has a speed of 0.8 knots (0.4 ms), the outcome again can be calculated from (18) as:
H = 57000 x 0.4 x sin 45[degrees]/67254 = 0.24 m (or, H = 57000 x 0.8 x sin 45[degrees]/130732 = 0.24 m).
Current speeds decrease after the water starts rising above Mean Water Level, and the movement correspondingly accelerates less. When acceleration to the right has ceased, the velocity to the right has to be counteracted by an opposite acceleration, either by the water moving in the opposite direction, or by the slope caused by the Coriolis effect. Eventually the water accumulated on the right side will start to move to the left. This movement causes a residual anticlockwise movement of the water in the Bay of Fundy and the Gulf of Maine as recorded by the movements of drift bottles. The phenomenon has been attributed to freshwater discharge of tributary rivers. However, compared with the tidal exchange, freshwater discharge is minuscule and of little account in the generation of residual currents.
The distance between Cape Cod and Cape Sable along the great circle is 414 km. The current speed in the Northeast Channel and over the Georges Bank may reach 2 knots or 1 [ms.sup.-1]. Theoretically, water levels at the Nova Scotia side could be more than 4 m higher (H = 414000 x 2 sin 42.5[degrees]/130732 = 4.28 m) than at Cape Cod when the water surface is near mean water level. Near High Water the currents are not as strong and the Coriolis gradient correspondingly less. However it seems likely that the Coriolis effect contributes to much stronger tides along the Gulf of Maine coastline of Nova Scotia than near Cape Cod and the Great South Channel (between Nantucket Shoals and Georges Bank). The range of the tides on the Nova Scotia side varies between 2 m on the Atlantic Ocean side to 4.5 m near the entrance to the Bay of Fundy, while on the Cape Cod side it varies between 0.5 and 1.0 m. Even at the head of the Bay of Fundy there is a substantial Coriolis effect on water levels. For example, hydrographic charts show that in the 5300 m wide Minas Channel, currents of 8 knots can occur. This means that on one side of the Channel the water levels could be about 0.23 m higher (H = 53000 x 8 x sin 45[degrees]/130732 = 0.23 m) than at the other side, because of Coriolis gradients.
The swing of the Coriolis effect with incoming tides might therefore be expected to exert a relatively stronger erosive power on southern or southeastern shores of channels and estuaries in the Bay of Fundy than ebb tides do on the opposite sides. In estuaries, of course, this swing is in the opposite sense to that of stream flow. Therefore, in Bay of Fundy estuaries at such times as stream discharge is relatively high, lateral mixing of fresh water and saline water will be promoted by the Coriolis effect.
The Coriolis effect is joined by the constraining effect of landmasses in imposing amphidromic systems on the tides (Fig. 8). Amphidromic systems occur in individual basins, seas, and lakes, for example the Gulf of St. Lawrence, or Lake Geneva on the border of Switzerland and France. In the elongated Lake Geneva, a gravitational forces cause a seiche, with alternately higher levels at one side than the other. In the Gulf of St. Lawrence, which is a more rounded body of water, the tidal movement is generated and kept going mainly by the ocean tides that enter through the Cabot Strait, with higher levels being at the right-hand side of the inflow. This results in the surface of the entire Gulf resembling a wobbling plate on a flat surface, with the highest (or lowest) rim of the plate rotating anticlockwise. In both cases the dimensions of the bodies of water must be such that a harmonic oscillation can take place, in the Gulf, the Coriolis effect causes a tidal wave to move anticlockwise, being high in the Cabot Strait when the ocean tide peaks. Dynamic tidal analysis thus treats tides as standing waves. The tides themselves are generally classified in terms of the ratio of the total amplitudes of the two principal diurnal components to the total amplitudes of the two principal semidiurnal components (for details see Fig. 4-3 in Desplanque and Mossman 1998a).
[FIGURE 8 OMITTED]
When the declination of the Moon is at its maximum value of 28.96[degrees], the Moon at its average distance from Earth will cause a maximum clockwise displacement of water particles around the poles of 438.5 m. If there were no Coriolis effect (i.e. if Earth were not rotating) the radius of the circular movement would be 146.1 m. The Coriolis effect thus tends to increase substantially the clockwise movements in the Northern Hemisphere, especially at points closer the North Pole. It has a much lesser effect on the anticlockwise movements that occur just north of the Equator. It is nil at the Equator, and maximum at the poles.
Note that although in the ocean basins anticlockwise motion of tide waves about amphidromic points occurs in the Northern Hemisphere, and vice versa in the Southern Hemisphere, several exceptions exist. The reason for these exceptions lies in the behaviour of the cotidal lines linking two amphidromic points. An example occurs in the southeastern Atlantic-western Indian Ocean system; here, as eloquently illustrated by Railsback (1991), amphidromic points linked by cotidal lines are likened to intermeshed gears (Fig. 9), and as such must necessarily rotate in opposite directions. This concept is particularly useful in explaining the anomalous sweep of the tides in low latitude systems.
[FIGURE 9 OMITTED]
Table 1. Wave speeds calculated at different wave length/depth ratios. m=L/D c c/[(g x D).sup.0.5] c/[(g x K).sup.0.5] 0.1 0.395 x [D.sup.0.5] 0.13 1.00 short waves 0.5 0.883 x [D.sup.0.5] 0.28 1.00 (deep water) 1 1.249 x [D.sup.0.5] 0.40 1.00 2 1.763 x [D.sup.0.5] 0.56 1.00 5 2.576 x [D.sup.0.5] 0.82 0.92 6.25 2.730 x [D.sup.0.5] 0.87 0.87 10 2.948 x [D.sup.0.5] 0.94 0.75 100 3.129 x [D.sup.0.5] 0.99 0.25 long waves 1000 3.131 x [D.sup.0.5] 1.00 0.07 (shallow water) Table 2. Characteristics of a tide wave with a 12.4 hour period and an amplitude of 0.45 m Particle Depth Wave Wave Particle speed displacement length speed amplitude amplitude D L c u' u' u (m) (km) (m/s) (m/s) (km/hr) (m) 5000 9916 221.4 0.02 0.072 142 1000 4434 99 0.04 0.160 318 200 1983 44.3 0.10 0.369 710 50 992 22.1 0.20 0.717 1420 10 443 9.9 0.45 1.604 3176 Table 3. Constituents in the Gulf of Maine--Bay of Fundy--Georges Bank system (in metres) [M.sub.2] [S.sub.2] [N.sub.2] [K.sub.2] (SD) Atlantic Ocean Station 22B 0.441 0.090 0.112 0.45 Gulf of Maine Portland 1.353 0.213 0.289 0.057 1.38 Pulpit Harbor 1.492 0.237 0.320 0.065 1.49 Bar Harbor 1.546 0.253 0.356 1.58 Eastport 2.613 0.426 0.526 0.116 2.67 Bay of Fundy Saint John 3.076 0.503 0.659 0.143 3.14 Partridge Island 3.085 0.509 0.597 0.137 3.14 Cape Blomidon 5.029 0.732 1.006 0.198 5.11 Parrsboro 5.051 0.753 0.847 0.204 5.12 Five Islands 5.400 0.831 1.129 0.226 5.51 Hantsport 5.665 0.847 0.722 0.236 5.73 Burntcoat Head 5.642 0.832 1.097 0.226 5.73 [K.sub.1] [P.sub.1] [O.sub.1] (DL) [K.sub.4] Atlantic Ocean Station 22B 0.075 0.209 Gulf of Maine Portland 0.146 0.044 0.155 0.063 Pulpit Harbor 0.139 0.047 0.111 0.007 Bar Harbor 0.140 0.110 Eastport 0.146 0.044 0.115 0.063 Bay of Fundy Saint John 0.153 0.049 0.119 0.18 0.057 Partridge Island 0.162 0.055 0.107 0.18 0.040 Cape Blomidon 0.162 0.055 0.116 0.18 0.046 Parrsboro 0.192 0.073 0.128 0.21 0.091 Five Islands 0.181 0.058 0.129 0.20 0.023 Hantsport 0.209 0.065 0.152 0.24 0.192 Burntcoat Head 0.143 0.049 0.122 0.18 0.101 Notes. SD = average amplitude of semidiurnal tides; DL = average amplitude of diurnal tides; [M.sub.2] = principal lunar; [S.sub.2] = principal solar; [N.sub.2] = longer lunar elliptic; [K.sub.2] = lunisolar semidiurnal; [K.sub.1] = lunisolar diurnal declination; [O.sub.1] = principal lunar diurnal; [P.sub.1] = principal solar diurnal; [K.sub.4] = lunar quarter-diurnal
2. Regional Tides
2.1. TERMS OF REFERENCE
Defant (1958) described tides, colourfully, as "... the heartbeat of the ocean, a pulse that can be felt all over the world." More technically, "tide" is the periodic rise and fall of the ocean surface in response to gravitational forces of the Moon and Sun. The periodicity of the tides is imposed by astronomical cycles determined by the relative motions of the Earth, Moon, and Sun. The regularity of tidal movements makes accurate prediction possible, and sets tides apart from other changes in sea level and from irregular phenomena like earthquakes, storms, and volcanic eruptions. In practice, tides are a mixture of diurnal (daily) variations, with one low and one high tide each day, and semidiurnal (twice daily) variation with two low and two high tides each day. In relatively shallow coastal waters these motions are of course greatly magnified. The "range" of the tides generally refers to the vertical movement of the water surface between the Low Water and the High Water levels of the tide. This factor, and the regime or mixture of the two types of tides varies from one area to another and also over time at any given location.
In Canada, the tidal levels in use (Canadian Tide and Current Tables 2004) are:
MWL--Mean Water Level--average of all hourly water levels observed over the available period of record; in comparison, Mean Sea Level (MSL) is a statistically established entity.
HHWLT--Higher High Water, large tide--average of the highest high waters, one from each of 19 years of predictions.
HHWMT--Higher High Water, mean tide--average of all the higher high waters from 19 years of predictions.
LLWMT--Low Low Water, mean tide--average of all the lower low waters from 19 years of predictions.
LLWLT--Lower Low Water, large tide--average of lowest low waters, one from each of 19 years of predictions.
LNT--Lowest Normal Tide--in present usage it is synonymous with LLWLT, but on older charts it may refer to a variety of low water chart datums--it is also called Chart Datum (CD), a most important term of reference.
All tidal measurements are made from the local Chart Datum (CD), an elevation so low that the tide at that place will seldom if ever fall below it. Thus, soundings on hydrographic charts show mariners the minimum depth of water. The tidal range gives them an extra margin of safety. Generally the tidal range is small and so is the margin of safety. However, for the Bay of Fundy, on charts showing a number of tidal stations, the difference between Chart Datum and Mean Water Level in one section of the charted area may be quite different than it is in other sections. The soundings on such charts do not allow one to construct a proper three-dimensional picture of the shape of the Bay. On land, the datum used by geodesists, surveyors, and engineers is the Geodetic Survey of Canada Datum (GSCD, or GD). This datum is based on the value of mean sea level prior to 1910 as determined from a period of observations at tide stations at Halifax and Yarmouth, N.S., and Pointe au-Pere, Quebec, on the east coast, and Prince Rupert, Vancouver, and Victoria, British Columbia, on the west coast. In 1922 the datum was adjusted in the Canadian levelling network. Because in most areas of the Maritime Provinces the landmass is submerging relative to mean sea level, geodetic datum drops gradually below mean sea level. However, there is a dearth of data, and no one is certain exactly what the difference is between GSCD and MWL at different stations. This situation is troublesome for engineers and biologists who need to know the proper relation between the two datums at particular places.
2.2. OVERVIEW OF REGIONAL TIDES ALONG THE EASTERN CANADIAN SEABOARD
Between the Atlantic Ocean and the eastern seaboard of the North American continent lies the continental shelf. In large measure a result of planation during the ongoing Pleistocene-Holocene Ice Age, the continental shelf has depths of less than 250 m. Near Cape Breton Island, it extends more than 200 km from the coast, although near the southern tip of Nova Scotia it narrows to 130 km (Fader et al. 1977). Farther south, along the coast of the United States, the shelf varies between 25 and 200 km. Off the continental shelf the seabed drops to depths of 5000 m over a distance of about 200 km. This 200 km-wide margin is known as the continental slope. Along the outer edge of the shelf the average tide ranges between 80 and 100 cm. After crossing the continental shelf, the tidal range along the shore of Nova Scotia is increased to between 120 and 140 cm.
When the relative positions of the Earth, Moon, and Sun generate exceptionally large tides, the tidal range along the shoreline of Nova Scotia may reach as high as 200 cm. This increase is 40-50% above average. Conversely, when the relative positions of the Earth, Moon, and Sun are such that tides are weakened, ranges drop by about 40% below the average. Variations in tidal strength of 60% to 140% are observed in the Gulf of Maine and the Bay of Fundy (Fairbridge 1966).
Between the Gulf of Maine and the Bay of Fundy, along the edge of the continental shelf off southwestern Nova Scotia and Cape Cod, Massachusetts, a series of shoals and banks acts as a sill obstructing tidal flow (see Fig. 3); in places the water is barely 4 m deep. Three channels cross this sill, of which the Northeast Channel is by far the largest between ocean and Gulf. Located between Georges Bank and Browns Bank, it is 230 m deep, 40 km wide, and 70 km long.
Tides on the ocean side of the Northeast Channel have an average range of 90 cm, but 320 km eastward at Bar Harbor, Maine, they have a mean range of 310 cm. High Water on this part of the coast is 3 hours later than along the edge of the continental shelf. The strength of tides in the southern bight of the Gulf of Maine, up to Race Point off Cape Cod, is rather uniform, varying between 210 and 310 cm for average tides; however between Bar Harbor and Jonesport 50 km to the east, their strength steadily increases toward the upper reaches of the Bay of Fundy. The average tidal range at the entrances to Minas Basin, Cumberland Basin, and Shepody Bay, each about 320 km from Bar Harbor, is 960 cm. However, in the Minas Basin the tides are 100 minutes later than at Bar Harbor. Tidal ranges are greatest in the estuaries of the Salmon and Shubenacadie rivers in the Minas Basin, 400 km from Bar Harbor. Depending upon astronomical conditions, this average range increases to 1360 cm. To the dismay of many inhabitants along this coast, even this enormous tidal range may be greatly extended by storm conditions.
2.3. GRAPHICAL SYNTHESIS OF REGIONAL TIDES
Figure 10 (see separate pull-out) shows the tidal ranges along the eastern Canadian seaboard during mean and large tides. At most places the tide reaches a maximum level on an average interval of 12.4 hours. Usually one of the two daily High Waters is higher than the other and is called the Higher High Water. Similarly, a Lower High Water and a Lower Low Water occur during a day-long tidal cycle. The distance that the tide moves up or down from the Mean Water Level is called the amplitude of the tide, and the total vertical distance between High Water and Low Water is the tidal range. The range given in the Canadian tide tables for a given locality is specifically for the distance between Higher High Water and Lower Low Water. This gives a somewhat larger value than ranges listed in American tide tables, which are calculated from the mean of the semidiurnal tides.
[FIGURE 10 OMITTED]
The center line of the band representing the tidal ranges (Fig. 10) depicts the local Mean Water Level; the pair of lines closest to this center line delineates the range during average tidal fluctuations in the area, and the outer pair delineates the fluctuation during large tides. Large tides occur when the main tide-producing astronomical forces are at maximum strength and working more or less in unison. The rise in feet of the Higher High Water above Mean Water Level during large and mean tides, and the fall of the Lower Low Waters below that datum, are shown on the chart beside the inserts which indicate the tidal characteristics near the principal tidal stations in the region.
Along the eastern Canadian seaboard the tidal ranges are rather uniform at 4 to 5 feet (1.22-1.52 m). The smallest tidal ranges in the charted area are recorded on the west coast of the Magdalen Islands and in the western Northumberland Strait, with mean ranges of 1.5 and 2.0 feet (0.45 m and 0.61 m). However in embayments such as the Bay of Fundy, the Bay of Chaleur, the channel leading to the St Lawrence River estuary, and the eastern and central parts of the Northumberland Strait, tidal ranges gradually increase at points more distant from ocean tides (White and Johns 1977).
Tidal characteristics near the principal, or reference, ports (e.g., Halifax, North Sydney) are included as marigrams in Fig. 10. The examples show the predicted tidal movements for March, 1966, a date chosen arbitrarily, the particular astronomical conditions for which are given with the sample set in the legend (inset at lower left of Fig. 10). The marigrams for this month are typical of any monthly period except that the sinusoidal diurnal and semidiurnal variations are offset according to astronomical conditions. In order to accentuate these characteristics, different vertical scales are employed. For this reason the local tidal amplitudes of Higher High and Lower Low Water during large and average tides are printed to the left of the inserts (see "Typical Tidal Variations over one Month"). Note that ranges are largest shortly after full moon and new moon during spring tides. When the Moon shows its quarter phases, the amplitudes are small and the tides are neap. The influence of the distance of the Moon from the Earth is such that when the Moon is in perigee (closest to Earth), spring tides are higher than when the Moon is in apogee (farthest from Earth). The diurnal inequality between high waters and low waters is nil when the Moon moves through the plane of Earth's equator, and as seen from Earth, reaches its peak when the Moon is in its most northerly or southerly position in the sky.
Local tidal characteristics along the eastern Canadian seaboard result from a combination of diurnal tides and semidiurnal tides. The diurnal tide repeats itself every 24.8 hours, and the semidiurnal tide every 12.4 hours (see insert, lower left hand side of Fig. 10). At most locations the semidiurnal tide is dominant. An exception is in the southern Gulf of St. Lawrence where, under certain astronomical conditions, only one High Water and one Low Water occur daily; here semidiurnal tides may have less than half the range of the diurnal component. Diurnal tides dominate along the north coast of Prince Edward Island, the west coast of the Magdalen Islands, and in the western portion of the Northumberland Strait.
Tidal characteristics also depend on the phase relationship between the diurnal and semidiurnal components. This manifests itself prominently in the Gulf of St. Lawrence where the strengths of both components are similar. Here there is less variation than in the Fundy tides, and there is no annual progression of 1.5 months in the highest tides. Tides in the Gulf of St. Lawrence tended to be higher in 1969 and 1973 (Fig. 11), years of relatively low tides in the Bay of Fundy (Canadian Hydrographic Service 1964, 1969a, 1969b, 1973, 1979, 1981).
[FIGURE 11 OMITTED]
Several other interesting contrasts exist among regional tides, in the Gulf of St Lawrence, when the High Water of a diurnal tide coincides with one of the two High Waters of the semidiurnal tide, the Higher High Water of the day is higher than the Lower High Water, assuming that the semidiurnal tide dominates at the location. This situation is because the other semidiurnal peak will coincide with the diurnal Low Water. Under these conditions the semidiurnal Low Waters will occur when the diurnal tide is near Mean Water Level and both will drop to almost the same level. This combination occurs in the western section of the Gulf of St. Lawrence (Fig. 10) where the High Waters at Rustico, P.E.I., Portage Island, N.B., and Pointe St. Pierre, Quebec, are usually unequal, in contrast to the almost equal Low Waters. (In Fig. 10 this is shown on the inserts indicating tidal characteristics near certain ports.) Note too, in Fig. 11, that the highest tides in the Gulf of St. Lawrence occur at mid-year and at year end, contradicting the age-old notion that equinoctial tides (March and September) will be the larger tides. Conditions similar to those of the Gulf of St. Lawrence prevail along the east coast of Newfoundland near St. John's and Argentia. The opposite conditions prevail in the Northumberland Strait where one of the semidiurnal Low Waters nearly coincides with the diurnal Low Water resulting in generally unequal Low Waters and almost equal High Waters (e.g., at Charlottetown, P.E.I., Pictou, N.S., and Shediac, N.B.). As shown in Fig. 12, for Halifax, North Sydney, and Charlottetown, the winter tides are predicted to be higher than summer tides. Note, too, that the Low Waters of Charlottetown extend much further below MSL than the High Waters reach above this level. This is because of the diurnal inequality of the tides, which causes High Water to be nearly the same each day and Low Water level to vary.
[FIGURE 12 OMITTED]
As a result of the Coriolis effect, in large bodies of water such as the North Atlantic Ocean and the Gulf of St. Lawrence, the tides and especially the semidiurnal tides circulate along the surrounding coastlines in an anti-clockwise progression forming an amphidromic system. At and near the system's central point the tidal range is nil. The location of the amphidromic system in the Gulf of St. Lawrence is shown in Fig. 10. Farther removed from the central point the tidal range gradually increases. Illustrating this progression the chart shows (in lunar hours, 1 to 12) the approximate positions of High Water of the semidiurnal component of the tide in this system. This semidiurnal system splits at the western side of the Northumberland Strait, one wave going directly into the Strait and the other traveling around Prince Edward Island and moving partly into the eastern entrance of the Strait; as it moves westward to Shediac Bay (see Fig. 10), it meets the wave trough of the one entering the west entrance. The result is that the semidiurnal tide is scarcely noticeable in this area, and so the diurnal tide becomes dominant. Only when the Moon is near the Equator will semidiurnal tides be observed.
Tides in the Gulf of St. Lawrence are generated and maintained by tidal movements in the Atlantic Ocean. The two systems appear to be synchronized, with simultaneous High Waters and simultaneous Low Waters at their meeting place in the Cabot Strait. Thus, the diurnal tide in the Gulf maintains a see-saw relationship with that of the Atlantic Ocean, being high in the Gulf when it is low in the ocean. The Coriolis effect causes the diurnal tides to peak in the northeastern part of the Gulf before they reach their maximum level along the southwestern coastline.
2.4. ADDITIONAL CONSIDERATIONS
During spring and summer in the Bay of Fundy and in the Northumberland Strait, the Lower Low Water occurs during the daytime (and HLW at night!) so that the tidal flats absorb considerable heat from the Sun. As the tide rises over the warm tidal flats, the water temperature rises, especially in the Northumberland Strait where the water cover is comparatively thin.
During the same seasons, in the western section of the Gulf of St. Lawrence the Lower High Water occurs during the daytime, covering to a limited depth the Sun-heated beaches and shoals with almost the same temperature-raising effects as occur along the Northumberland Strait. This has ecological implications. For example, both sections of the Gulf have a mollusc fauna similar to that found near Virginia along the eastern U.S. seaboard. The species involved need a water temperature above 68[degrees]F (20[degrees]C) to spawn. Yet, even during the warmest months of the year the mean air temperature in the Gulf is less than this value. Tidal characteristics of the area are therefore probably important factors in the propagation of these species in this part of the Gulf.
Conditions are reversed during fall and winter, exposing tidal flats to heat loss at Lower Low Water during the night. This results in the following Lower High Water being cooled well below normal sea water temperature as it flows over these frigid flats, circumstances that probably aggravate ice conditions.
A tidal wave with a period of about 12.4 hours appears in the Atlantic Ocean in front of the Gulf of Maine, causing a wave to enter through the Northeast Channel. The wave propagates over the Gulf, reaching the shore about three hours later. As this progressive wave moves along the mouth of the Bay of Fundy, a standing wave is formed, and energy becomes concentrated toward the head of the Bay as its cross-sectional area is gradually reduced.
A standing wave can form in a basin in which the water moves periodically from one side to the other, high water at one side corresponding to low water on the other. The strength of the tide is strongest at the ends of the basin. Although in the center of the basin the water surface does not move up and down, strong currents are present because a large volume of water must move to and fro in order to create the High Water alternately at both ends.
The funnel-shaped Bay of Fundy branches at its northeast end into the Minas Basin and Chignecto Bay. The dimensions of the Bay of Fundy are such that its natural period of oscillation closely approximates that of the semidiurnal tidal component, thus greatly increasing resonance. There are fascinating variations on this theme. For example, as detailed in section 1.4.3 (on applications to tides and water currents), due to the Coriolis effect the entering tidal stream is deflected toward the southern shore of the Bay and the retreating stream to the north.
On average, the up and down sweep of the tide solely due to the Coriolis effect is larger on the Nova Scotia side for the incoming tide than for the outgoing tide on the corresponding opposite New Brunswick shore (see Fig. 13). Thus, when the water reaches its highest level (A), the tide is still coming in, filling the upper reaches of the Bay, and the water maintains a lateral slope AB (Fig. 13a). At the turn of the tide, it is level (BC), although the level on the Nova Scotia side will have already dropped (A to C). Note that, like the sweep of the tidal level due to the Coriolis effect, the range of the incoming tide in any Fundy cross-section is higher perpendicular to the axis of the Bay on the Nova Scotia side. Likewise, tidal flow entering the Gulf of Maine, results in a higher tidal range on the Nova Scotia side. The same argument applies to any cross-section as the tide ebbs (Fig. 13b). Approaching the turn of the tide, the water continues flowing seaward for some time, just as it still has kinetic energy which allows it to flow upward to higher level (D) on the New Brunswick side than on the Nova Scotia side (F). At the turn of the tide, it is level (DE).
[FIGURE 13 OMITTED]
Thus, the south shore experiences a greater tidal range than does the north shore, as well as a counter-clockwise system of residual tidal currents (see Fig. 13). Turbulent current in the narrow strait between Minas Channel and the Minas Basin can exceed 11 knots.
In the upper reaches of the Bay of Fundy, the standing wave fills the estuaries. However, the rate of rise of tide is so rapid that large flows of water into the mouths of the estuaries would be required if the water surface in the estuaries were to rise at the same rate as in the Bay. Because the estuarine cross-sections are relatively small, particularly at low tide, such large flows of water are not able to enter. Therefore, filling of the estuaries is delayed. Physical restrictions on flow velocities are much more severe in shallow water than in deep water. The result is that water flowing in the more shallow parts is overtaken in time by water which, although entering the estuary later, moves faster in the deeper water. Thus, on the gently sloping bottom of the estuary a tidal bore commonly develops, most impressively so when the tide has its largest amplitude.
Theoretically, in basins where a standing wave occurs, hardly any currents are at the end where the tides are strongest. However, if there are shallow estuaries to be filled, strong tidal currents will develop in a relatively short time. These currents are the main agents of transportation and deposition of sedimentary materials in the Bay.
High Water occurs progressively later further up the estuaries. This High Water can happen quite a distance up the estuary, and considerably later than the time of High Water at the mouth. The time differential depends in turn on the gradient of the estuary bottom within the tidal range. As we shall see (section 9.5), these two factors are intimately linked to the evolution of the tidal marshes within estuaries in the Bay of Fundy.
2.5. A SUCCESSION OF STANDING AND PROGRESSIVE WAVES
A profound difference exists between the tidal regime of the Gulf of St. Lawrence and that of the Bay of Fundy. This much is evident in the frequencies and occurrence of monthly maximum and minimum tidal water levels. Predicted tide water levels over typical 8- and 10-year intervals are shown for three ports in, respectively, the Gulf of St. Lawrence (Fig. 11) and the Atlantic coast (Fig. 12). Note that in all years the highest High Waters for Charlottetown, Halifax, and North Sydney (i.e., the Atlantic coast) were predicted around the winter solstice (Fig. 12), whereas the lowest Low Waters occurred near the summer solstice. However, for the three ports in the Gulf of St. Lawrence (Fig. 11), the highest High Waters and the lowest Low Waters occurred near the solstices, but with no noticeable difference between those near the winter solstice and those near the summer one. The smallest ranges of the tides were predicted to occur near the equinoxes.
The above relationships clearly demonstrate that the tidal regime along the Atlantic coast is different from that in the Gulf of St. Lawrence. Both are unlike the one in the Bay of Fundy. While in most waters, the largest tides occur in the same part of the year, in the Bay of Fundy they are more influenced by the shifting coincidence of spring and perigean tides with the result that each year they occur about 47 days later than in the previous year. Overall, regional tides along the eastern Canadian seaboard are best described as a succession of standing and progressive waves. The standing waves occur in the Atlantic Ocean, the Gulf of St. Lawrence, and the main body of the Bay of Fundy, whereas the progressive waves occur in the Gulf of Maine, the upper reaches of the Bay of Fundy, and in the estuaries leading into the Gulf and Bay. Progressive waves, unless supplied by external sources of energy such as air currents, do not grow in strength, for they lose energy when moving through confining channels. Likewise, progressive waves entering a restricted harbour mouth lose strength when they expand over the wider harbour surface. However, as we shall see, the wave entering the Gulf of Maine through the Northeast Channel seems to gain in strength while spreading over the Gulf. In fact it becomes 3.5 times stronger on reaching the shoreline.
3. Tides of the North Atlantic
3.1. WATER PARTICLE MOVEMENTS
According to Pliny the Elder, writing in his Historia naturalis: "... tides swell more during the equinoxes, more during the autumn than in the spring, but ... were empty at midwinter and even more so at midsummer". Unknown to Pliny, the tides are much complicated by the shape of the oceanic basins. The example of conditions prevailing in the North Atlantic on 5 September, 1975, with the new moon in perigee (and rather small declinations of the Sun, 6.5[degrees], and Moon, 5.8[degrees]) serves very well to illustrate (Clancy 1969). With the Moon closest to Earth on its monthly orbit, higher than normal tides can be expected. The theoretical movements of individual particles in the ocean on this date (for details see Desplanque and Mossman 1998a) are rather small, clockwise, and predominantly diurnal. Nevertheless, the tides on that day were large. Table 4 provides the times and heights of the tides as they were predicted to be at sixteen ports along the eastern seaboard of the North American continent.
Do movements of the North Atlantic ocean follow water particle movements generated locally, or are they a result of an oscillating motion of the ocean with a period of 12.4 hours? First let us compare the times of High Water with the location of water particles in their cycle near 45[degrees] N latitude.
Table 4 shows that the highest tides on the western side of the Atlantic reach the highest levels of the day between 18:45 and 20:49 AST (moving from north to south, as indicated by the theoretical particle movements calculated for that day). The smaller high tides for that day occurred between 6:30 and 8:30 AST.
Semidiurnal tides are predominant in the Atlantic Ocean, the diurnal component being small (Fairbridge 1966). On the eastern side of the Atlantic (Table 5), the diurnal inequality of the tide is small. The High Waters from Morocco to France (about 15[degrees]N and 45[degrees]N latitude respectively) occur between 9:40 and 11:35 AST (13:40-15:35 GMT) and 22:00 and 24:50 AST (2:00-4:00 GMT), the tidal wave moving from south to north (Schwiderski 1980). These times coincide closely with those for the easternmost locations of water particles (Desplanque and Mossman 1998a).
Given the Atlantic Ocean's 5000 km width and 5000 m depth, a scale model of this ocean as an oscillating basin would be approximately 1 m square and 1 mm deep. As it turns out, such a model is unrealistic (see Kwong et al. 1997) although it clearly illustrates the shallowness of the ocean. For example, if the ocean is oscillating, then when the water is high at one side of the ocean it should be low at the other side. So, if it is high between 9:40 and 11:40 AST (Table 5) at the eastern side one should expect it to be low at the same time on the western side. However, according to Table 4, low tide occurs in the west between 12:25 and 14:29. It appears, therefore, that ocean tides are more in tune with water particle movements than with an oscillating system.
3.2. TIDAL CONSTITUENTS AND HARMONIC ANALYSIS
Except for the Gulf of Maine and the Bay of Fundy, the ranges of tides on the eastern side of the Atlantic Ocean are substantially greater than those along the North American coast (Apel 1987). Harmonic analysis, the principle first applied to tidal problems by Lord Kelvin (1824-1907), is the most satisfactory method of comparing characteristics of tides observed at various locations (Schureman 1941, 1949; Fairbridge 1966). This method relies on the fact that the observed tide is the result of several astronomically driven partial tides. Just as complicated sea waves can be reconstructed by combining several wave trains, so also can tides be calculated by combining partial tides, or tidal constituents. For most ports bordering the North Atlantic Ocean (Desplanque and Mossman 1998a), the [M.sub.2] constituent is dominant (see Table 3; Fig. 14).
[FIGURE 14 OMITTED]
Since 1977, tidal records have been collected along the edge of the continental shelf off North America, and more recently at several stations in the mid-Atlantic between Newfoundland and Portugal. Tables 6 and 7 show the results of analyses of these data together with data from shore stations. The ranges of the major constituents at these stations are given and the strength of other constituents is compared with [M.sub.2]. This can be used to determine if the local [S.sub.2] tide is close to its theoretical strength of 46% of the [M.sub.2] strength.
The value of the initial phase p (known as the phase lag and representing the phase of the constituent at the time of origin) is given as the epoch (Table 6), based on the local meridian of the observation station, and the 65[degrees]30, W meridian. The use of the latter as a time meridian is prompted by the fact that this meridian crosses the main entrance of the Gulf of Maine and also the entrance of the Bay of Fundy. Note in Table 6 that the percentage of [S.sub.2]/[M.sub.2] is close to the theoretical value of 46% near Newfoundland, but slightly less in the eastern North Atlantic. The relative strength of the [N.sub.2] constituents remains close to 22%, while the already weak diurnal [K.sub.1] and [O.sub.1] constituents are even weaker in mid-ocean. One might expect that the tidal wave would follow the apparent westerly movements of agents that account for the existence of the various constituents. However the phase lags indicate that the co-tidal lines move from west to east, in the opposite direction of the imaginary heavenly bodies.
Table 7 shows the same type of data for ports along the eastern seaboard of North America, with additional data from some stations offshore. Indications are that the time of High Water is virtually the same for all stations over a distance of 2200 km between Banquereau Bank, south of the Cabot Strait, and Charleston, South Carolina. The strength of the Sun's influence is much less than the theoretical 46% of the Moon's influence, dropping from 24% at the Banquereau Bank to 17% at Charleston. Again there is little change in the relative strength of the [N.sub.2] constituent. Thus, variations in the tidal strength caused by the variable distance between Earth and Moon gain in significance over variations in the influence of the Sun's gravitation. Stated otherwise, the perigean tides become more important than the spring tides.
The influence of the Sun is far more noticeable along the coast of Newfoundland and Labrador. The percentage of [S.sub.2] with respect to [M.sub.2] ranges from 36% on the south coast of the Avalon Peninsula, north of the Cabot Strait, to 68% near Fogo Island at the northeast corner of Newfoundland. It drops again to 50% near the northern tip of the island, and to 36% along the Labrador coast. Evidently tides near Newfoundland have characteristics in common with those in the mid and eastern North Atlantic whereas tides south of the Cabot Strait have a different pattern.
3.3. EQUINOCTIAL TIDES: EAST VERSUS WEST
Other characteristics also indicate that tides between Newfoundland and Europe are of a different regime than those along the North American mainland. One of these characteristics concerns the stronger equinoctial tides. Plinys oft quoted statement probably accounts for the assumption by most oceanographers that the so-called equinoctial tides (March and September) reach higher levels than tides close to the solstices (June and December). Pliny may have been correct, for he was only aware of tides that can be observed on the east side of the Atlantic Ocean. Table 8 shows the highest predicted tides for each month in 1953 and 1975 for stations on the east side of the Atlantic. The semi-annual peaks are underlined. These data support Pliny's claim that the tides near the equinoxes are generally higher than those occurring during the remainder of the year. Even the fall tides are stronger than those in the spring, and the midwinter ones are stronger than the midsummer ones. However, as shown below, Pliny's claim is not valid along the east coast of North America, or along the continent's west coast south of the Alaskan panhandle.
Data for 1953 and 1975 from stations on the west side of the Atlantic (Table 9) are rather less supportive of Pliny's case. However, in order to test for possible bias in the two sample years, Table 10 supplies a more complete set of data for Halifax. Note that the peak tides do not fall in the same months as they did on the other side of the ocean, and that they are spread over all seasons. The only month in which no peak occurs is September, one of the equinox months. Each successive year the peak appears to arrive somewhat later. This can be explained by the dominance of perigean tides on the west side of the ocean. The Spring Tide cycle has a period of 14.77 days, and the perigean cycle one of 27.56 days. After 205.89 days, these cycles overlap each other causing interference and extraordinary strong tides. Every second overlap occurs the following year, but 47 days later in the season. It is, therefore, incorrect to claim that on the western side of the ocean the equinoctial tides are the highest tides of the year. The highest tides of the year occur in the late fall and early winter season, because the mean water levels are higher in winter than in summer due to world-wide shifts in atmospheric pressures. Another phenomenon discernible in Table 10 (last column) is that every 4 to 5 years the tides reach another peak. This peak occurs because after 112 cycles of Moon declinations, their peaks occur again at almost the same time. The result is a 4.53 year cycle of extraordinary high tides.
As discussed earlier, the theoretical movements of water particles in the oceans, due to the direct gravitational effects of the Moon and Sun, generally result in diurnal loops. Only during either new or full moon close to the equinoxes do strictly semidiurnal movements occur near the Equator. During fall and winter the most westerly displacements are reached during the morning hours, and during spring and summer in the evening hours. The diurnal inequality of tides along the North American seaboard shows the same tendency. During the summer months the most easterly displacements are reached around 04:00 and 05:00 hours local time, and during the winter, around 16:00 and 17:00 hours. As shown in Table 11 the tidal observations along the eastern side of the ocean are not in step with these particle movements. Clearly, tidal characteristics on the eastern side of the Atlantic differ significantly from those on the western side. It seems likely that the North American ocean basin, with its Sohm, Hatteras, and Nares abyssal plains, enjoys its own tidal regime, distant from that of the basins between Newfoundland and Europe.
We turn now to the behaviour of tidal waters along the coast of northern New England where North Atlantic tides impinge on the Gulf of Maine and the Bay of Fundy.
Table 4. Tides predicted for 5 September, 1975, along the eastern seaboard of North America Low Water High Water AST m+CD AST m+CD St. John's, NF 0020 0.24 0630 1.07 Argentia, NF 0045 0.36 0700 2.29 Point Tupper, NS 0100 0.43 0650 2.26 Halifax, NS 0110 0.21 0705 2.10 Yarmouth, NS 0315 0.09 0935 4.51 Saint John, NB 0430 0.18 1040 8.14 Eastport, Ma. 0447 -0.73 1053 6.22 Portland, Ma. 0450 -0.40 1102 3.08 Boston, Mass. 0507 -0.46 1117 2.87 Newport, R.I. 0112 -0.21 0746 1.40 New York, N.Y. 0226 -0.18 0830 1.68 Sandy Hook, N.J. 0152 -0.21 0758 1.74 Charleston, S.C. 0156 -0.15 0808 1.89 Savannah Harb., Ga. 0205 -0.21 0812 2.53 Mayport, Fla. 0204 -0.06 0825 1.88 Miami Harb., Fla. 0203 -0.09 0815 1.01 Low Water High Water AST m+CD AST m+CD St. John's, NF 1225 0.15 1845 1.37 Argentia, NF 1255 0.27 1920 2.56 Point Tupper, NS 1335 0.46 1915 2.19 Halifax, NS 1330 0.34 1920 2.16 Yarmouth, NS 1540 0.18 2205 4.79 Saint John, NB 1700 0.24 2300 8.50 Eastport, Ma. 1711 -0.76 2315 6.49 Portland, Ma. 1711 -0.37 2325 3.29 Boston, Mass. 1726 -0.43 2339 3.51 Newport, R.I. 1336 -0.24 2011 1.43 New York, N.Y. 1448 -0.18 2049 1.80 Sandy Hook, N.J. 1409 -0.21 2016 1.83 Charleston, S.C. 1417 -0.24 2018 2.01 Savannah Harb., Ga. 1429 -0.30 2033 2.71 Mayport, Fla. 1425 -0.18 2051 1.77 Miami Harb., Fla. 1429 -0.09 2041 1.01 Notes. Times are given in Atlantic Standard Time (AST) (z + 4). All heights are measured in metres above the Chart Datum at each port. Tides in the Gulf of Maine, e.g., Yarmouth to Boston, are secondary movements caused by the Atlantic tide, and they occur about three hours later than the Atlantic tide. Data from U.S. Department of Commerce (1953, 1975) Table 5. Tides predicted for 5 September, 1975, along the west coast of North Africa and Europe Low Water High Water Low Water High Water AST m+CD AST m+CD AST m+CD AST m+CD Dakar, Senegal 2156 0.55 0416 1.74 1031 0.34 1641 1.74 Casablanca, Moroc. 0322 0.64 0939 3.90 1551 0.49 2204 3.81 Gibraltar 0311 0.03 0948 1.11 1533 0.03 2205 1.10 Lisbon, Portugal 0405 0.37 1045 4.18 1633 0.21 2310 4.05 Point de Grave, Fr. 0432 1.16 1056 5.24 1657 0.94 2400 5.60 Brest, France 0532 1.16 1135 7.80 1754 0.85 2357 7.80 Queenstown, Eire 0733 -0.12 1259 3.84 1928 -0.18 2518 3.90 Reykjavik, Iceland 0752 0.00 1358 4.24 2017 -0.12 2625 4.05 Notes. Times are given in Atlantic Standard Time (z + 4). All heights are measured in metres from the Chart Datum at each port. Data from U.S. Department of Commerce (1975.) Table 6. Characteristics of the tides, measured at mid-Atlantic stations between St. John's Newfoundland, and Lisbon, Station Constituent [M.sub.2] [N.sub.2] [S.sub.2] St. John's 1.= 46[degrees]34' 5.= 70 14 29 2.= 52[degrees]42' 6.= 100 20 41 3.= 7.= 210 192 254 4.= 8.= -5.98 -6.63 -4.46 [A.sub.1] 1.= 46[degrees]04' 5.= 30 6 14 2.= 46[degrees]34' 6.= 100 21 46 3.= 495 7.= 238 238 284 4.= 515 8.= -5.42 -5.48 -3.85 [B.sub.1] 1.= 45[degrees]59' 5.= 29 6 13 2.= 46[degrees]27' 6.= 100 21 46 3.= 507 7.= 249 239 285 4.= 667 8.= -5.05 -5.42 -3.82 [B.sub.2] 1.= 44[degrees]29' 5.= 30 7 13 2.= 40[degrees]27' 6.= 100 23 44 3.= 1001 7.= 310 298 325 4.= 2380 8.= -3.36 -3.76 -2.9 [A.sub.3] 1.= 43[degrees]06' 5.= 49 11 18 2.= 35[degrees]11' 6.= 100 23 36 3.= 1451 7.= 347 333 1 4.= 3460 8.= -2.47 -2.92 -2.06 [A.sub.4] 1.= 34[degrees]13' 5.= 79 17 32 2.= 28[degrees]55' 6.= 100 21 40 3.= 2473 7.= 348 337 4 4.= 3525 8.= -2.86 -3.22 -2.37 [A.sub.5] 1.= 43[degrees]02' 5.= 127 28 42 2.= 21[degrees]52' 6.= 100 22 33 3.= 2446 7.= 41 24 65 4.= 2480 8.= -1.52 -2.05 -0.82 [D.sub.11] 1.= 45[degrees]01' 5.= 175 37 59 2.= 21[degrees]52' 6.= 100 21 33 3.= 2850 7.= 66 44 90 4.= 2830 8.= -1.22 -1.8 -0.39 Lisbon 1.= 38[degrees]41' 5.= 233 60 91 2.= 9[degrees]06' 6.= 100 25 39 3.= 3621 7.= 59 41 83 4.= 8.= -1.77 -2.35 -1.06 Station Constituent [K.sub.1] [O.sub.1] St. John's 1.= 46[degrees]34' 5.= 16 14 2.= 52[degrees]42' 6.= 23 20 3.= 7.= 107 74 4.= 8.= 6.19 4.63 [A.sub.1] 1.= 46[degrees]04' 5.= 12 8 2.= 46[degrees]34' 6.= 41 27 3.= 495 7.= 111 90 4.= 515 8.= 6.04 5.39 [B.sub.1] 1.= 45[degrees]59' 5.= 13 8 2.= 46[degrees]27' 6.= 44 25 3.= 507 7.= 110 90 4.= 667 8.= 5.94 5.35 [B.sub.2] 1.= 44[degrees]29' 5.= 10 4 2.= 40[degrees]27' 6.= 34 14 3.= 1001 7.= 100 83 4.= 2380 8.= 4.88 4.43 [A.sub.3] 1.= 43[degrees]06' 5.= 9 2 2.= 35[degrees]11' 6.= 18 4 3.= 1451 7.= 86 23 4.= 3460 8.= 3.64 -0.23 [A.sub.4] 1.= 34[degrees]13' 5.= 7 5 2.= 28[degrees]55' 6.= 10 6 3.= 2473 7.= 44 271 4.= 3525 8.= 0.39 -8.75 [A.sub.5] 1.= 43[degrees]02' 5.= 12 7 2.= 21[degrees]52' 6.= 9 5 3.= 2446 7.= 69 314 4.= 2480 8.= 1.59 -6.12 [D.sub.11] 1.= 45[degrees]01' 5.= 14 11 2.= 21[degrees]52' 6.= 8 6 3.= 2850 7.= 74 320 4.= 2830 8.= 1.52 -6.21 Lisbon 1.= 38[degrees]41' 5.= 25 12 2.= 9[degrees]06' 6.= 10 5 3.= 3621 7.= 39 309 4.= 8.= -1.24 -7.44 Notes. For each station are given: 1, latitude-north; 2, longitude-west; 3, distance (km) from St. John's, Newfoundland; 4, depth (m) at each station; 5, range (cm) of the 5 major constituents; 6, percentage of constituent's strength to [M.sub.2] tide; 7, epoch (degrees); 8, phase lag (hours) from 66[degrees]30' meridian. Table 7. Characteristics of the tides as measured along the edge of the continental shelf and at some ports along the east coast of North America Station Constituent [M.sub.2] [N.sub.2] [S.sub.2] St. John's 1.= 46[degrees]34' 5.= 70 14 29 2.= 52[degrees]42' 6.= 100 20 41 3.= 1188 7.= 210 192 254 4.= 8.= -5.98 -6.63 -4.46 St. Brides, Nfld 1.= 46[degrees]55' 5.= 139 29 50 2.= 54[degrees]11' 6.= 100 20 36 3.= 1055 7.= 224 200 262 4.= 8.= -5.38 -6.24 -4.1 Banquereau 1.= 44[degrees]35' 5.= 88 20 21 2.= 57[degrees]41' 6.= 100 22 24 3.= 701 7.= 230 205 262 4.= 64 8.= -4.95 -5.84 -3.47 Sable Island 1.= 43[degrees]35' 5.= 105 18 23 2.= 58[degrees]46' 6.= 100 17 22 3.= 519 7.= 232 213 269 4.= 8.= -4.71 -5.38 -3.67 B1 1.= 42[degrees]48' 5.= 97 24 21 2.= 63[degrees]12' 6.= 100 25 20 3.= 216 7.= 224 200 257 4.= 226 8.= -4.78 -5.63 -3.67 22B 1.= 42[degrees]03' 5.= 88 22 18 2.= 65[degrees]38' 6.= 100 25 20 3.= 0 7.= 210 219 263 4.= 242 8.= -4.12 -4.84 -3.37 T23 1.= 40[degrees]22' 5.= 81 21 17 2.= 67[degrees]45' 6.= 100 24 21 3.= -257 7.= 221 201 245 4.= 174 8.= -4.57 -5.28 -3.77 Kelvin 1.= 39[degrees]56' 5.= 87 21 18 2.= 71[degrees]00' 6.= 100 24 21 3.= -511 7.= 206 190 235 4.= ? 8.= -4.81 -5.42 -3.87 Sandy Hook 1.= 40[degrees]27' 5.= 135 31 26 2.= 74[degrees]10' 6.= 100 22 19 3.= -721 7.= 218 201 246 4.= 8.= -4.23 -4.82 -3.3 Atlantic City 1.= 39[degrees]21' 5.= 117 27 24 2.= 74[degrees]26' 6.= 100 23 19 3.= -799 7.= 207 190 231 4.= 8.= -4.58 -5.18 -3.77 Charleston 1.= 32[degrees]46' 5.= 145 33 25 2.= 79[degrees]56' 6.= 100 22 17 3.= -1495 7.= 210 200 246 4.= 8.= -4.23 -4.58 -3.04 Station Constituent [K.sub.1] [O.sub.1] St. John's 1.= 46[degrees]34' 5.= 16 14 2.= 52[degrees]42' 6.= 23 20 3.= 1188 7.= 107 74 4.= 8.= 6.19 4.63 St. Brides, Nfld 1.= 46[degrees]55' 5.= 12 15 2.= 54[degrees]11' 6.= 8 11 3.= 1055 7.= 122 113 4.= 8.= 7.13 7.53 Banquereau 1.= 44[degrees]35' 5.= 11 9 2.= 57[degrees]41' 6.= 12 11 3.= 701 7.= 104 108 4.= 64 8.= 6.34 7.47 Sable Island 1.= 43[degrees]35' 5.= 5 5 2.= 58[degrees]46' 6.= 5 5 3.= 519 7.= 102 151 4.= 8.= 6.34 10.7 B1 1.= 42[degrees]48' 5.= 14 11 2.= 63[degrees]12' 6.= 14 11 3.= 216 7.= 109 113 4.= 226 8.= 7 8.26 22B 1.= 42[degrees]03' 5.= 15 11 2.= 65[degrees]38' 6.= 17 12 3.= 0 7.= 110 116 4.= 242 8.= 7.2 8.51 T23 1.= 40[degrees]22' 5.= 15 12 2.= 67[degrees]45' 6.= 19 15 3.= -257 7.= 112 112 4.= 174 8.= 7.1 8.48 Kelvin 1.= 39[degrees]56' 5.= 17 14 2.= 71[degrees]00' 6.= 20 16 3.= -511 7.= 107 110 4.= ? 8.= 7.4 8.55 Sandy Hook 1.= 40[degrees]27' 5.= 20 10 2.= 74[degrees]10' 6.= 15 8 3.= -721 7.= 102 98 4.= 8.= 7.27 7.9 Atlantic City 1.= 39[degrees]21' 5.= 21 15 2.= 74[degrees]26' 6.= 18 13 3.= -799 7.= 107 91 4.= 8.= 7.63 7.43 Charleston 1.= 32[degrees]46' 5.= 21 15 2.= 79[degrees]56' 6.= 14 10 3.= -1495 7.= 126 126 4.= 8.= 3.13 10.19 Notes. Legend as for Table 6 except for item 3, distance (km) from station 22B (Northeast Channel). Table 8. Highest High Water predicted for each month for ports on the eastern side of the North Atlantic Ocean Year J F M A M J Casablanca 1953 12.5 12.8# 12.8# 12.5 12.1 12.1 1975 13.0# 13.0# 12.5 11.8 11.5 11.6 Gibraltar 1953 3.9 4.0 4.1# 4.0 3.9 3.7 1975 3.4# 3.3 3.2 3.1 3.0 3.0 Lisbon 1953 13.1 13.6 13.7# 13.4 12.9 12.6 1975 13.6 13.8# 13.6 13.2 12.8 12.6 Cordouan 1953 17.4 18.2# 18.2# 17.6 16.1 15.9 Pointe de Grave 1975 19.2 19.5# 19.2 18.2 17.4 17.1 Brest 1953 25.8 26.4 26.7# 25.9 24.3 24.0 1975 26.4 26.8# 26.4 25.4 24.3 24.0 Southampton 1953 14.2 14.7 14.8# 14.4 13.7 13.0 1975 15.9 16.1# 15.9 15.2 14.9 14.5 Liverpool 1953 31.1 32.1# 31.9 31.0 28.1 29.2 1975 33.1 33.4# 32.9 31.6 30.6 30.2 Queenstown 1953 12.4 12.8 12.9# 12.8 12.2 11.8 1975 12.7 12.8# 12.8# 12.6 12.2 11.7 Reykjavik 1953 14.2 14.6# 14.5 14.1 13.6 13.5 1975 14.6# 14.2 13.4 13.1 12.9 13.1 Distribution of Peaks 2.5 9.0 6.5 Average Height 14.6 16.8# 16.6 16.1 15.4 15.2 Year J A S O N D Casablanca 1953 12.5 12.8# 12.8# 12.5 12.1 12.1 1975 12.3 13.0 13.1# 13.1# 12.6 12.3 Gibraltar 1953 3.9 4.0 4.1# 4.1 3.9 3.7 1975 3.3 3.6 3.7# 3.7# 3.5 3.3 Lisbon 1953 13.3 13.8 13.9# 13.6 13.1 12.9 1975 12.8 13.5 14.0 14.1# 13.8 13.5 Cordouan 1953 17.1 18.2 18.5# 17.7 16.7 16.1 Pointe de Grave 1975 18.0 19.0 19.5# 19.5# 18.9 18.0 Brest 1953 25.4 26.7 26.9# 26.2 25.1 24.3 1975 25.1 26.2 26.9# 26.7 25.9 23.8 Southampton 1953 13.3 14.6 14.7# 14.5 14.1 13.4 1975 15.1 15.7 16.0 16.1# 15.7 15.2 Liverpool 1953 30.7 32.0 32.0 31.1 29.4 28.6 1975 31.7 32.9 33.4# 33.1 32.4 31.4 Queenstown 1953 12.5 13.0 13.5# 13.4 12.9 12.1 1975 12.2 12.8 13.6 13.6# 13.4 12.8 Reykjavik 1953 14.3 14.6# 14.5 14.2 13.8 13.5 1975 13.7 14.2 14.4# 14.2 14.3 14.2 Distribution of Peaks 2.0 11.5 4.5 Average Height 15.9 16.7 17.0# 16.7 16.2 15.9 Notes. Heights measured in feet from local Chart Datum. Semi-annual peak tides underlined. Note: Semi-annual peak tides indicated with #. Table 9. Highest High Water predicted for each month for ports on the western side of the North Atlantic Ocean Year J F M A M J Argentia 1953 6.6# 6.4 6.1 6.2# 5.9 5.7 1975 8.3# 8.1 7.8 7.9 8.0# 7.9 Halifax 1953 7.3 7.3 7.4# 7.2 7.1 6.8 1975 7.6# 7.6# 7.5 7.3 7.0 6.9 Newport 1953 4.3 4.3 4.5 4.7# 4.6 4.5 1975 4.5 4.6 4.8# 4.8# 4.7 4.5 New York 1953 5.3 5.3 5.5 5.7 5.8# 5.6 1975 5.5 5.4 5.7 5.9# 5.8 5.6 Breakwater 1953 5.4 5.3 5.3 5.5# 5.4 5.1 1975 5.2 5.0 5.3 5.4# 5.4# 5.2 Washington 1953 3.0 3.2 3.2 3.7# 3.6 3.5 1975 3.1 3.1 3.3 3.6# 3.6# 3.5 Charleston 1953 6.1 6.0 6.2 6.5# 6.4 6.2 1975 6.2 6.1 6.5 6.6# 6.4 6.2 Miami 1953 2.8 2.8 3.0 3.1# 3.0 2.7 1975 2.8 2.9 3.1# 3.1# 2.9 2.7 Distribution of Peaks 2.0 0.5 2.5 10.0 3.0 Year J A S O N D Argentia 1953 5.9 6.0 6.4 6.7# 6.7# 6.4 1975 8.2 8.4 8.5 8.5 8.6# 8.4 Halifax 1953 6.9 7.2 7.5 7.7# 7.5 7.2 1975 7.0 7.2 7.4 7.6# 7.6# 7.5 Newport 1953 4.5 4.7 4.9# 4.9# 4.7 4.4 1975 4.6 4.7 4.5 5.0# 4.9 4.7 New York 1953 5.7 5.8 5.9 6.0# 5.7 5.3 1975 5.7 5.9 5.9 6.1# 6.0 5.7 Breakwater 1953 5.2 5.2 5.0 5.6 5.6# 5.3 1975 5.3 5.4 5.4 5.7# 5.7# 5.4 Washington 1953 3.6 3.3 3.9# 3.7 3.4 3.0 1975 3.5 3.6 3.6 3.8# 3.6 3.2 Charleston 1953 6.2 6.3 6.8 7.0# 6.7 6.2 1975 6.3 6.5 6.7 7.0# 7.0# 6.6 Miami 1953 2.9 3.2 3.6 3.7# 3.5 3.0 1975 2.8 3.0 3.5 3.7# 3.7# 3.3 Distribution of Peaks 1.5 10.0 3.5 Notes. Heights measured in feet from local Chart Datum. Semi-annual peak tides underlined. Note: Semi-annual peak tides indicated with #. Table 10. Highest High Water predicted for each month for the port of Halifax, Nova Scotia Year J F M A M J 1953 7.3 7.3 7.4* 7.3 7.1 6.8 1954 6.8 7.0 7.2 7.4* 7.3 7.1 1955 7.2 6.9 7.1 7.3* 7.3* 7.1 1956 7.3 7.0 6.9 6.7 7.0 7.1 1957 7.3 7.3 7.3 7.2 6.9 6.8 1958 7.1 7.2 7.4* 7.4* 7.3 7.1 1959 7.1 7.0 7.2 7.4* 7.3 7.2 1960 7.3 6.9 6.8 6.7 7.2* 7.2* 1961 7.4 7.3 7.1 7.0 6.9 7.1 1962 7.2 7.3* 7.3* 7.3* 7.2 7.0 1963 7.0 7.1 7.2 7.4* 7.4* 7.1 1964 7.2 6.7 6.9 7.1 7.3* 7.3* 1965 7.3 7.1 6.8 6.8 7.0* 7.0* 1966 7.2* 7.2* 7.2* 7.2* 7.0 6.8 1967 7.4 7.5 7.6* 7.4 7.1 6.8 1968 7.3 7.3 7.4* 7.4* 7.2 7.0 1969 7.6 7.4 7.2 7.1 7.3* 7.3* 1970 7.3 (7.5) (7.5) 7.4 7.2 7.2 1971 7.5 7.6 (7.7) 7.6 7.3 6.9 1972 7.4 7.2 7.3 7.4* 7.4* 7.3 1973 7.5 7.1 7.0 7.0 7.0 7.1* 1974 (7.8) 7.5 7.3 6.9 6.8 7.1 1975 7.6 7.6 7.5 7.3 7.0 6.9 1976 6.8 7.2 7.5 7.7 (7.8) 7.6 1977 6.9 7.1 7.3 7.5 7.6* 7.5 1978 (7.6) 7.4 7.0 7.3 7.4* 7.4* 1979 (7.7) 7.5 7.5 7.4 7.2 7.4 1980 7.6 7.7 7.8* 7.8* 7.6 7.3 1981 7.4 7.3 7.6 7.7* 7.7* 7.6 1982 7.7 7.6 7.3 7.5* 7.5* 7.4 1983 (7.8) 7.7 7.5 7.2 7.2 7.2 1984 7.3 7.6 7.8* 7.7 7.5 7.1 1985 7.2 7.5 7.7 7.8# 7.7 7.4 Year J A S O N D Maximum 1953 6.9 7.1 7.5 (7.7) 7.5 7.2 7.7* 1954 6.7 6.8 7.2 7.5 (7.6) 7.5 7.6 1955 6.9 6.8 6.8 7.1 (7.6) 7.5 7.6 1956 7.1 7.1 7.1 7.2 7.2 (7.4) 7.4 1957 7.0 7.2 7.4 (7.5) 7.3 7.0 7.5 1958 6.7 6.9 7.3 7.6 (7.7) 7.5 7.7 1959 6.9 6.7 6.8 7.2 7.6 (7.7) 7.7* 1960 7.2* 7.1 7.0 7.1 7.4 (7.5) 7.5 1961 7.1 7.2 7.3 (7.4) 7.2 7.1 7.4 1962 6.8 7.0 7.3 (7.6) (7.6) 7.4 7.6 1963 6.8 6.6 6.9 7.3 7.6 (7.7) 7.7* 1964 7.1 6.9 6.8 7.3 (7.5) (7.5) 7.5 1965 6.9 7.0 7.1 (7.2) 7.0 (7.2) 7.2 1966 6.8 7.0 7.3 7.3 (7.4) 7.2 7.4 1967 6.7 7.0 7.4 7.7 (7.8) 7.7 7.8* 1968 6.9 6.9 7.3 7.6 (7.7) 7.6 7.7 1969 7.1 7.1 7.2 7.3 7.4 (7.6) 7.6 1970 7.2 7.1 7.4 (7.5) (7.5) 7.4 7.5 1971 6.9 7.0 7.3 7.6 (7.7) (7.7) 7.7 1972 7.1 6.9 7.4 7.7 (7.8) (7.8) 7.8* 1973 7.1* 6.9 7.0 7.2 7.5 (7.8) 7.8* 1974 7.2 7.2 7.3 7.4 7.4 7.7* 7.8* 1975 7.0 7.2 7.4 (7.6) (7.6) 7.5 7.6 1976 7.7 (7.8) 7.6 7.4 7.5# 7.4 7.8 1977 7.3 6.9 6.8 7.5 7.8 (7.9) 7.9* 1978 7.2 7.1 7.0 7.1 7.5 (7.6) 7.6 1979 7.4 7.4 7.5 7.6* 7.6* 7.5 7.7 1980 7.1 7.4 7.7 (7.9) (7.9) 7.7 7.9* 1981 7.3 7.1 7.4 7.7 7.8 (7.9) 7.9* 1982 7.3 7.3 7.3 7.4 7.5 (7.8) 7.8 1983 7.3 7.4 7.5 7.7* 7.6 7.5 7.8 1984 7.2 7.4 7.8 (7.9) 7.8 7.5 7.9* 1985 7.0 7.2 7.6 7.8 (7.9) 7.7 7.9* Notes. Heights measured in feet from local Chart Datum; values between brackets are the highest of the year. Values underlined are the higher of the other semiannual peak, and the pioridicity over the years (underlined) is shown in the last column. Note: Values are the higher of the other semiannual peak, and the pioridicity over the years (underlined) is shown in the last column indicated with *. Table 11. Diurnal inequality during solstices in 1953 on both sides of the North Atlantic Ocean 21 June, 1953 20 December, 1953 Time Local Local Local Local Zone Time m+CD Time m+CD Time m+CD Time m+CD St. John's 3.5 0743 0.82 1942 1.19* 0706 1.37* 1937 1.19 Halifax 4 0812 1.83 2008 2.01* 0720 2.10* 2008 2.01 New York 5 0810 1.25 2029 1.68* 0752 1.62* 2021 1.22 Miami 5 0747 0.73 2032 0.82* 0750 0.91* 1954 0.82 Dakar 0 0841 1.58* 2105 1.49 0822 1.49 2044 1.71 Casablanca 0 0156 3.29 1415 3.60* 0135 3.60* 1402 3.51 Lisbon 0 0316 3.41 1537 3.72* 0245 3.81* 1512 3.66 Brest 0 0350 6.74 1612 7.04* 0325 7.25* 1549 7.16 Note. Highest High Waters are underlined. Note. Highest High Waters are indicated with *.
CON DESPLANQUE (1) AND DAVID J. MOSSMAN (2) *
(1.) 27 Harding Avenue, Amherst, NS B4H 2A8
(2.) Department of Geography, Mount Allison University, 144 Main St., Sackville, NB E4L 1A7
* Corresponding author
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|Title Annotation:||Part 1: Preface-Chapter 3|
|Author:||Desplanque, Con; Mossman, David J.|
|Date:||Mar 1, 2004|
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