Tides and their seminal impact on the geology, geography, history, and socio-economics of the Bay of Fundy, eastern Canada.
11.1. INTRODUCTION: THE SAROS CYCLE
Pytheas, a navigator from the Greek colony of Massalia (modern Marseilles, France), explored the northern Atlantic Ocean in the Fourth Century B.C.E. Proceeding north after passing between the Pillars of Hercules, he noticed the lengthening of the summer days and observed the midnight Sun in Thule, a six day voyage north of Britain. He was aware too, of the relationship between tides and the Moon's motion along its orbit.
Pliny the Elder (23-70 A.D.) mentioned in his Historia Naturalis that, according to Pytheas, the tides north of Britain rise to heights of 120 feet ("octogenis cubitis"). The notion of the existence of such enormous tides persists. For example, the eminent 19th Century scientists Sir John Herschel and Sir Oliver Lodge repeated the belief that 120 foot-high tides occur in the Bay of Fundy. Only a few years ago the same misconception was linked to the extraordinarily high tides associated with the so-called "Saxby Gale".
One might wonder where the extraordinary high tides occurred that so impressed Pytheas. He must have been familiar with the 40 foot-high (12.19 m) tides that regularly occur along the Brittany coast on the French side of the English Channel, or in the Bristol Channel south of Wales. According to the Roman writer Festus Avienus, these waters were visited a century before by Himilco, a famous Phoenician explorer, and by merchantmen trading for tin. The only other tides in the North Atlantic of the same order of magnitude are the 30 ft (9.14 m) tides in the White Sea portion of the Arctic Ocean, and the more than 40 ft (12.19 m) tides in Ungava Bay, Quebec and the Bay of Fundy. The White Sea can only be reached by waters lying north of the Arctic circle where the midnight Sun can be observed in midsummer. Could Phoenician seafarers have reached the western side of the Atlantic and, after visiting the Bay of Fundy, passed to Pytheas the notion of 120 foot-high tides?
As we have seen, tides are caused by the attraction of the Moon and Sun on water particles near the surface of the Earth. Since the orbits of the Moon around the Earth, and of the Earth around the Sun, are elliptical, the effects are variable in strength, like the resulting tides. The redeeming feature is that every aspect of each motion has a corresponding periodicity to which tidal variations can be related. The pages-long equation describing the paths of celestial bodies, a masterpiece of human ingenuity, was first set out by Louis Lagrange (1736-1813) and Pierre Simon de Laplace (1749-1827). Yet even the ancients possessed considerable knowledge concerning these matters.
Nearly four centuries before Pytheas described the influence that the Moon's motions have on the tides, Chaldean priests in the Middle East were able to predict recurrence of eclipses. This was because of their knowledge of the Saros, a Babylonian name adopted by modern astronomers for a cycle with a period of 18 years, 11 days and 8 hours. In this 18.03-year cycle, the Moon, Sun, and Earth return to almost identical relative positions to each other. This is the cycle in which similar solar and lunar eclipses repeat themselves. Eclipses result when the Sun, Moon, and Earth are in, or almost in, one straight line.
The paths of the solar eclipses over the Earth's surface are almost identical in shape, but are located 110[degrees] to 130[degrees] west of the path of the eclipse of 18 years previous (Abell et al. 1988). For example, one series of solar eclipses began on 17 May, 1501 (Julian calendar), as a partial eclipse. (At present, 12 such series producing total solar eclipses occur during a Saros cycle of 18.03 years). After 15 Saros cycles with partial and annular eclipses, the eclipse became total on 6 November, 1771. The total eclipse seen on 7 March, 1970, over Mexico, the USA and Canada was one of the series; likewise that of 18 March, 1988 as seen over the Pacific, Sumatra and Borneo (see Fig. 66). After this, there will be 35 more total eclipses followed by half a dozen partial ones. All told, the Saros prediction is valid for 1226 years [(1988-1501) + (35+6). 18.03 = 1226.23 years)] for this particular series.
[FIGURE 66 OMITTED]
Because the astronomical conditions conducive to generating large tides match the Saros cycle, their recurrence at 18.03 year intervals is expected. Could it be that this particular timing is closely linked to the occurrence of exceptionally high tides like the Saxby Tide? There is good suggestive evidence that this is the case, but first we need to look further into the causes of tides and their variations. Only then will we better appreciate the implications of the Saros for a future tide comparable to the Saxby.
11.2. ASTRONOMY AND THE VARIATIONS OF TIDES
Orbital forcing of tidal cycles is only a small portion of the spectrum (Fig. 67) of astronomically-driven periods which exert gravitational effects on Earth and the affairs of humankind (Rampino et al. 1987). The same periodic behaviour governs changes over time in the energy distribution reaching Earth's atmosphere, and must have done so throughout geologic time. We are concerned here only with tidal phenomena within a small portion of the calendar and solar frequency bands.
[FIGURE 67 OMITTED]
S.M.Saxby might have added to his prediction that the great storm tide destined to immortalize him, especially in the view of many Maritimers, would coincide with the Saros (Desplanque 1974). In this 18.03 year cycle, Moon, Sun and Earth return to almost identical relative positions. It is astounding to realize that by 800 B.C., Chaldean priests knew the Saros well enough to accurately predict eclipses. Could it be that eclipses, or more particularly the time interval between eclipses, might be associated with far higher than normal tides?
In general, the average gravitational effect of the Sun is about 46 percent that of the Moon; however, in the Bay of Fundy the effect of the Sun is only about 15 percent that of the Moon. Further, because the orbits of the Earth around the Sun and the Moon around the Earth are elliptical, and their paths influenced by many factors (Fig. 67), the gravitational effects are variable in strength, like tides (House 1995).
Normal tides are termed astronomical tides because their main variations are generated by three astronomical phenomena as noted earlier: the variable distance between the Moon and Earth; the variable positions of the Moon, Sun and Earth relative to each other; and the declination of the Moon and Sun relative to the Earth's equator. Additional astronomical factors that influence tides include: the Earth's rotation; the eccentricity of the Moon's orbit, which varies depending on the Sun's position in relation to the longest axis of the Moon's orbit.
Non-astronomical phenomena include: the possible increasing tidal range in places like the Bay of Fundy due to deepening waters (Godin 1992); atmospheric disturbances; the geometric shape of inlets, bays and ocean basins; the postglacial rise in sea level (see Fig. 68). This last factor, by no means trivial, translates to about a world-wide 2 mm/yr submergence of the land in relation to sea level (Schneider 1997).
[FIGURE 68 OMITTED]
11.3. THE LARGEST ASTRONOMICAL TIDES
As seen from Earth, the Moon and Sun seem to move within two imaginary rings around Earth's centre (Fig. 69). The ring in which the Moon's motions are confined has an outside diameter of 813 000 km and a maximum thickness of 50 000 km, while its width varies during an 18.61 year period between 410 000 km and 2.55 000 km. The Sun appears to move within a similar ring, with an outside diameter of 3.04.108 km, a maximum thickness of 5 x [10.sup.6] km, while its width remains constant at 1.25 x [10.sup.8] km. At perigee the distance to the Moon is 3.57 x [10.sup.5] km, and at apogee the distance is 4.07 x [10.sup.5] km.
[FIGURE 69 OMITTED]
The positions of the Sun and Moon in their respective (elliptical) orbits, and in relation to each other and the Earth, are only occasionally repeated. When one position is inducive to generating large tides, an approximate date for a repeat performance can be determined by matching the several types of astronomical months. Such months are designated as synodic, anomalistic, tropical, nodical or evectional, according to whether the revolution of the Moon around the Earth is relative to the Sun's position, the shortest distance to the Earth, its passing through the Earth's equator, its passing through the ecliptic, or the variation in the eccentricity of its orbit. For some months, such as the synodical (full and new moon), tropical, and nodical, the characteristics influencing the tides occur half-monthly. Since the synodical conditions provide the dominant tidal conditions, one can expect two sets of spring tides during one synodical month. But when one of these sets coincides with the Moon's closest approach to the Earth, extra high (perigean) spring tides will occur.
It takes 29.531 solar days between one new moon and the next. However, only 27.555 solar days (anomalistic month) elapse from the time that the Moon is closest to the Earth, to the next such occasion during the Moon's elliptical orbit around Earth. When the Moon is in perigee, and its phase is either full moon or new moon, one can expect the strongest tides. However, as the periods of both movements are not the same, the coincidence of such occurrences is only periodic.
Imagine a racetrack. On this track are two cars, marked N and F. They always move half a track apart around the raceway. Let the raceway be 360[degrees] long. Thus, each day, these cars move 360[degrees]/29.531 = 12.19[degrees]/day (V). Another car, marked P, starts at the same time beside car N, but its velocity is 360[degrees]/27.55 = 13.06[degrees]/day (W), thus somewhat faster than car N. In time, car P will overtake car F, which was 180[degrees] in front of car N. The time it will take to close this gap can be calculated (approximately) as 180/(W-V) = 205.892 days.
The same applies to lunar movements. After about 206 days, the conditions for stronger than average tides recur, perigee coinciding either with new moon or full moon. Two of these periods are 411.78 days long. Thus, each year one can expect the conditions for stronger tides to be (411.78-365) = 47 or 46 days (leap year) later than in the previous year.
The declination of the Moon also has an influence on the strength of the tides on particular days. This declination has its strongest values twice in a period of 27.321 solar days (tropical month) with a velocity of 360[degrees]/27.32 = 13.18[degrees]/day. This is somewhat faster than the velocity of the perigee. Therefore in order to have the coincidence of a similar combination between perigee and declination of the Moon, it will take 1615.75 days, or 4.42 years. Should a particular part of the declination cycle cause somewhat higher tides then the coincidence with perigee will repeat after 4.42 years. During the Saros cycle of 6585.32 days, there will be 238.997 perigee cycles, 446.01 (full moon-new moon) cycles, and 482.07 declination cycles.
The most favourable combination of factors to produce strong tides in the Bay of Fundy occurs when perigee coincides with spring tide at the very time that anomalistic, synodic and tropical months peak simultaneously. As it happens (see Table 22), the best match occurs after a period of 6585.3 days (18.03 years). The driving mechanism of this cyclic phenomenon is the same one that orders the timing of eclipses--the Saros.
11.4. COINCIDENCE OF STORM TIDES WITH SAROS
Given the clockwork precision of astronomical conditions and their absolute control over normal tide variations it is reasonable now for us to enquire whether the Saxby Tide, and for that matter other historical storm tides in the Bay of Fundy, coincided with the Saros.
What are the chances of a periodic storm system on the scale of the Saxby tide? The only certainty is that the relationships between the Moon and the Sun that produce the highest tides on Earth are repeated in the same periods as those that create solar and lunar eclipses (Abell et al. 1988), namely the Saros cycle of 18.03 years. Therefore, to check the position of an historical high tide in the Saros, one need only add to the tide's date the appropriate multiple of the Saros (Table 23) to reach a particular time interval for which the tidal record is well known. Detailed tidal records in Canada were first kept about 1894. So as a reference point let's choose a date close to the end of 1958, which is eleven Saros after the Saxby Tide. The tidal levels referred to are those measured at Saint John, where the average high tide is 7.7 m (25.2 feet) above CD. To test the reliability of the method of prediction, our examples of historical storm tides can now be checked against predicted tides, n Saros cycles later.
Checking the multiples of the Saros against storm tides, we discover that the storm tides of 1759 and 1869 correlate very closely with predicted high tides of the Saros cycle (Table 24). So do the 1976 Groundhog Day storm, and the exceptionally High Water of 12 October, 1887, experienced in Moncton, and the storm tides of 20-22 December, 1995 (Taylor et al. 1996). However, it is important to bear in mind through any exercise of this type that Saros cycles are long term harmonic motions. This means that near the top or bottom of the cycle the rate of change with time is relatively small. Thus, the "peaks" of Saros cycles are not confined to points in time, but to rather short intervals of time.
11.5. PROBABILITY OF A REPEAT OF THE SAXBY TIDE
Whether property owners along the Bay of Fundy should be reminded of their next appointment with the Saros in 2012-2013 AD is not trivial question (Fig. 70). With increasing encroachment of people in coastal zones, the risk of loss of life and major property damage in the Gulf of Maine-Bay of Fundy region is substantial in the event of a tide like the Saxby Tide (Shaw et al. 1994). Simply put, what is the probability of a storm tide coinciding with a large astronomical tide? We can conveniently address this question using the above examples. We know that a "peak" of the Saros occurred between 6 March, 1958, and 31 December, 1959. During this time, there were 1288 tides at Saint John, 37 of which were extreme astronomical high tides (28.5 feet or higher). Thus, the chances that an historically memorable storm tide coincided with one of the 1288 tides, is slightly less than 3 percent. This is assuming that the occurrence of stormy weather conditions is spread evenly throughout the year. The increased incidence of high winds during late spring and fall probably favours the odds of gale force conditions coincident with high tides slightly above 3 percent.
[FIGURE 70 OMITTED]
Most assuredly, postglacial sea-level rise is a significant factor in all this. With each and every repeat of the Saros, an increase of the high tide mark of at least 3.6 cm (2 mm/year for 18 years) can be expected. Thus, since the Saxby Tide more than seven Saros ago, sea level has risen eustatically nearly 25 cm. Added to the minimum 1.5 m by which the Saxby Tide exceeded high astronomical tides, a height is calculated that that is more than sufficient to overrun the present dyke system.
It seems likely that tides like the Saxby might be recurrent, although one wishes for a larger database. The clockwork precision of astronomical conditions exerts absolute control over normal tidal variations. But there remains much to learn about long term periodic events associated with tides and the weather. We have seen that only significant storms coincident with large tides, or extraordinarily severe storms coincident with medium tides, can result in higher tide marks than are reached by astronomical tides alone. Detailed tidal records over several decades show that in the Bay of Fundy there is a tendency for slightly higher maximum monthly High Water marks in a 4.5 year cycle, examples being the peaks that occurred in 1998 and 2002. Indeed, in this region, high perigean tides levels can be anticipated at intervals of 1 month, 7 months, 4.5 years and 18 years. When such high tide levels coincide with severe atmospheric disturbances, exceptionally High Water surfaces can be expected. However, short of an extraterrestrial catastrophe, they are not likely to attain the 120-foot (36.6 m) height of legend. Property owners along the Bay of Fundy should nevertheless keep in mind their next appointment with the Saros in 2012-2013.
Table 22. Long term cycles of astronomical conditions leading to stronger or weaker than normal tides Anomal. Synodic. Tropic. Nodical month month month month 27.5546 29.5306 27.3216 27.2122 days days days days Number of months or years Number of solar days 7 6.5 7 7 192.88 191.95 191.25 190.49 15 14 15 15 413.32 413.43 409.82 408.18 60 56 60.5 61 1653.27 1653.71 1652.95 1659.95 112 104 113 113.5 3086.11 3085.95 3087.34 3088.59 172 160 173 174 4739.38 4739.66 4740.29 4734.93 239 223 241 242 6585.54 6585.32 6584.50 6585.36 299 279 301.5 303 8238.81 8239.03 8237.46 8245.30 351 327 354 355 9671.65 9671.27 9671.84 9673.94 Number of months or years Number of solar days Evection Gregor. Eclipse period Stand. year year 31.8119 dev. 365.24 346.62 days days days days 6 0.528 0.556 190.87 1.63 13 1.131 1.192 413.56 3.49 52 4.526 4.769 1654.22 2.90 97 3085.76 1.20 149 12.975 13.673 4739.98 2.22 207 18.030 18.999 6585.07 0.40 259 22.557 23.768 8239.29 1.35 304 26.480 27.902 9670.83 1.20 Notes. Anomalistic month (cycle of perigean tides) = 27.555 days; synodic month (cycle of Moon's phases in which there are two sets of spring and neap tides) = 29.531 days; tropical month (cycle in which Moon crosses the Equator twice) = 27.322 days. Close match between multiples of anomalistic, synodic and tropical months coincides with repeated similar tidal conditions. A close match between synodical and nodical months are cycles for lunar and solar eclipses. (After Desplanque and Mossman, 1998a) Table 23. Multiples of the Saros Saros Years Days Cycle 1 18 11 Cycle 2 36 23 Cycle 3 54 34 Cycle 4 72 45 Cycle 5 90 57 Cycle 6 108 68 Cycle 7 126 79 Cycle 8 144 91 Cycle 9 172 102 Cycle 10 180 113 Cycle 11 198 125 Table 24. Countback of tides in the Bay of Fundy at 18.03-year intervals Comparison of the 1759 storm tide with the high tide at Saint John eleven Saros cycles later, on 8 March 1958: Day in the Date Year year Historical high tide 3 November 1759 1759 307 Add 11 Saros cycles (198 years 125 days) 198 125 1957 432 (1 yr 67 d) 8 March 1958 The predicted high tide for 8 March 1958 was 8.75 meters. Comparison of the Saxby Tide, 1869, with the high tide at Saint John five Saros cycles later, on 1 December 1959: Day in the Date Year year Saxby Tide 5 October 1869 1869 278 Add 5 Saros cycles (90 years 57 days) 90 57 1959 335 1 December 1959 The predicted high tide for 1 December 1959 was 8.84 meters. Notes. Calculations show that the historical storm tide of 3-4 November 1759 and the Saxby tide of 4-5 October 1869 closely coincide with predicted high tides of the Saros.
12. Tidal Boundary Problems in the Coastal Zone
12.1. INTRODUCTION: CAVEAT EMPTOR!
The need for precise determination of tidal water boundaries stems from numerous concerns, including cadastral surveying, coastal property evaluation, development of offshore resources, protection of fisheries, and ownership of the foreshore and sea bed (Nichols 1983; Daborn and Dadswell 1988). Historically, the dividing line between wet and dry land, or as far as the tide ebbs and flows, has been critical in resolving tidal boundary problems in the coastal zone (Ketchum 1972). However, the location of the mean high water line has been a matter of considerable litigation (Greulich 1979; Desplanque 1977). What exactly is this dividing line, and how can levels like Mean High Water and Mean Low Water be most accurately defined?
Presumably, Mean High Water is reached under mean astronomical conditions, with perhaps some long-term tectonic and climatological influences to be considered. Climatic influences in Atlantic Canada tend to raise the water during the winter months, so that in areas of relatively small astronomical tides along the Atlantic seaboard the frequency of extreme high observed water levels is higher during that season. However, astronomical influences are variable and follow cycles in which the magnitude of influences waxes and wanes (Schureman 1941). The longer the cycles, the greater the variation. In the Fundy region, as discussed earlier (section 11.0), distinct cycles are recognized (Desplanque and Bray 1986).
Meteorological influences can raise or lower water surface levels over a period of days, during which time High Waters and Low Waters are similarly affected. On a year long scale, climatic influences in the Atlantic region tend to raise the water level during winter months. Thus in areas of relatively small astronomical tides along the Atlantic coast of North America the frequency of extreme high observed water levels is higher during winter. The eustatic rise of sea level can not be neglected in these considerations: over the course of an 18 year cycle, accepting a global average 2 mm/yr eustatic rise in sea level (Schneider 1997), water level will have risen by about 3.5 cm. In view of the above considerations it appears that decisions handed down in courts of law on issues concerning tidal water boundaries are in many cases equivocal (Nichols 1983; Desplanque 1977).
Harvey et al. (1998) provided a very interesting analysis of the legal and policy framework concerning the restoration of the habitat of Fundy estuaries. Unfortunately, important overlapping boundaries of provincial and federal jurisdiction, in some cases unresolved, seem to have resulted in poorly regulated environmental protection. Details of the many issues of territorial and legislative jurisdiction, as they generally concern Bay of Fundy waters and the coastal zone, are beyond the scope of this paper. Nevertheless many of the key issues center on the problem of establishing specific water level boundaries.
12.2. MEASUREMENT OF TIDAL LEVELS
Concerning the tide levels and terms used in Canada (as set out in section 2.1), all tidal measurements are made from the local Chart Datum (CD). The International Hydrographic Bureau recommends that CD at a certain location should be at an elevation so low that the tide at that place will seldom if ever fall below it. The reason for this recommendation is that the soundings on hydrographic charts will show the minimum depth of water with which mariners will need to deal. The tidal range gives them an extra margin of safety. Generally tidal range is small and so is this factor in their margin of safety. However, on Bay of Fundy charts showing a number of tidal stations, the difference between CD and Mean Water Level (MWL) 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.
The Canadian Marine Sciences Branch defines mean sea level (MSL) as the level that oceanic water would assume when no atmospheric, hydrologic or tidal influences act upon it. They also use the term Mean Water Level (MWL), which is the sea level resulting in the absence of tidal influences. Up to certain limits the base level of the tides is moving up and down with the water level caused by atmospheric and hydrologic conditions. Since it is easier in the field to establish a local MSL or MWL than a level indicating the Mean High Water Mark (MHW), it is recommended that MHW be the level reached by the [M.sub.2] amplitude above MSL.
It is worth noting too that whereas the Canadian Tide and Current Tables give the values of tidal differences for Higher High Waters and Lower Low Waters, the U.S. Tide Tables give the values for Mean High Water (MHW) and Low High Water (LHW). Consequently, the values of the ranges for mean and large (spring) tides differ greatly in both tables for the same locations (see Table 25). The differences between these datums are significant to the problem of establishing tidal boundaries. Canada apparently lacks a definition of MHW, a level usually taken in surveying practice as equivalent to "Ordinary" High Water (OHW) (Nichols 1983). Britain's intertidal zone is also proving difficult to map due to use of different vertical scales by Ordnance Survey and the Admiralty's Hydrographic Office, and the fact that the latter organization uses "the lowest astronomical tide" as zero point for depth (Tickell 1995). The Americans take MHW as the average of all the High Water heights observed over the National Tidal Datum Epoch. For this reason American definitions are inappropriate for direct use in Canada.
Next let's examine how an accurate determination of the Mean High Water mark can be made.
12.3. TIDE PREDICTION: MEAN SEA LEVEL AND MEAN HIGH WATER
For most locations (ports) along the Canadian sea coast, the [M.sub.2] tidal constituent is dominant. In fact the amplitude of the [M.sub.2] tide very closely represents the average tidal conditions. When measured above the local MSL, it will indicate the level of MHW. The value of this amplitude has been determined for a great many ports along the Canadian sea coast. As for MSL, it can be easily determined by taking the average of hourly readings in calm conditions over one lunar day. The mean of these readings should indicate the MWL of the day. In order to verify if this level is close to MSL one can check at the nearest tidal recording station if the observed tides for that day correspond closely to the predicted ones. If so, the MWL can be used as a substitution for MSL. Otherwise a correction can he made by applying the difference to the measured value of MWL. Generally these differences (when they occur) are in the same order of magnitude for a number of recording tidal stations.
Since the Higher High Water (HHW), the Lower High Water (LHW), and the MWL values (see Table 26) above local CD are determined for a great number of stations along the eastern seaboard, the Mean High Water mark for most locations can be accurately determined with very little effort. A large degree of accuracy is not warranted because the landmass of the southern part of the Atlantic Provinces is steadily submerging at a rate matched by the rise of the High Water mark.
12.4. THE WATER'S EDGE: CONFUSION IN LEGISLATURE AND LITERATURE
As expressed in Canadian law, "The land on the seaward side of the high water mark is primafacie held by the sovereign in common law jurisdictions." In other words such land is generally owned by the state, i.e., in Canada, the provincial or federal government.
Some Nova Scotia acts, for example, reflect this principle (Kerr 1977). The 1967 Nova Scotia Beach Protection Act states that the Governor in Council, on recommendation of the Minister of Lands and Forests, may designate as protected beach, an area which "... may include the land extending seaward from mean high water mark and such land adjacent thereto ... The Minister of Lands and Forests may post signs on or near land of the Crown extending seaward from mean high water mark, warning the public that the beach is protected under this Act".
The 1975 Nova Scotia Beaches Preservation and Protection Act declares that "beach" means that area of land on the coastline to the seaward of Mean High Water mark, and that land landward immediately adjacent thereto, to the distance determined by the Governor in Council.
The 1949 Nova Scotia Marshland Reclamation Act interprets as "marshland" the land lying upon the sea coast or upon the bank of a tidal river, and being below the "level of the highest tide". Legislative practice assumes that the vertical and horizontal location of the Mean High Water mark, and the level of the highest tide are established and available all along the coastline. Unfortunately, confusion abounds in legal circles about the characteristics of the tides and the terminology used to describe them. For instance, in the upper reaches of the Bay of Fundy the tides can reach more than 8 m above MSL during strong tides, whereas during weak tides the High Water is scarcely 3 m above that level. Approximately 50% of the tides reach above the 5.5 m mark. Furthermore, the range varies from year to year and from location to location along the coast. Complicating matters is the fact that MSL changes even in the short term (Fairbridge 1987), at different rates in relation to the landmass, depending upon the location. Indeed, the concept of MSL is like Earth's Magnetic North Pole, elusive. Thus, in tide tables, the term Mean Water Level is used.
The confusion in legal circles is exemplified in "Water Law in Canada-The Atlantic Provinces" (La Forest 1972) where the three types of tide of which the law takes cognizance are described:
Tide type #1--high spring tide, which occurs at the two equinoxes;
Tide type #2--spring tide, which happens at the full moon and the change of the Moon;
Tide type #3--the neap, or ordinary tide, which takes place between full moon and change of the Moon, twice every twenty-four hours.
Unfortunately, because of three reasons discussed in the ensuing paragraphs, it is doubtful whether these types of tide have any significance along the eastern and western seaboards of the North American continent.
Firstly, Pliny the Elder (23-79 A.D.) observed that the tides appear to be the strongest in the periods close to the equinoxes, namely on 21 March and 23 September. This observation may well be true for tides along the eastern side of the North Atlantic Ocean. However, Pliny could not know that the conditions along the American coastline are different. Thus, Table 27 shows that although tides on the eastern side of the Atlantic are highest near the equinoxes, this is clearly not the case for tides along the eastern or western coastlines of North America. Note that the tides in 1953 and 1975 on the eastern seaboard of North America may reach their highest levels at any month of the year due to their advance by 47 or 46 days each year as a result of perigee coinciding with either new moon or full moon. The definition of tide type #1 implies that equinoctial tides are in a way special, but this rule is in no way universal.
Secondly, the term "change of the Moon" is archaic, and designates new moon. It means, simply, that tides occurring during the period that the Moon appears in its full moon and new moon phases are stronger than average tides. This is of course due to the fact that these phases of the Moon occur when the Earth, Sun and Moon are most closely aligned. At these times, the gravitational action of the Sun reinforces the action of the Moon, resulting in higher than average tides, just as is supposed to happen in type #1 tides. During its orbit, the Moon is in one of its two quarter phases when halfway between its new moon and full moon positions. At such times the gravitational action of the Sun counteracts the dominant Moon's action, resulting in neap tides.
Unfortunately, in legal circles European tidal conditions are taken as standard and assumed to be universal. Theoretically the Sun's action is close to 46% of the Moon's gravitational influence. However, when the tides are analyzed, the actual percentage can differ depending upon the locality. Some of the measured percentages on the east side of the Atlantic Ocean are: Casablanca 37%, Rabat 40%, Lisbon 39%, St. Nazaire 35%, Flushing 27%, Bremerhaven 25%, London 27%, Liverpool 32%, Kingstown 30%. These figures are the ratios between the local tidal constituents $2 and [M.sub.2] (Schureman 1941). Note that these percentages are smaller than the theoretical one. Nevertheless, they are relatively strong compared to those along the North American eastern seaboard south of Sable Island. Here the percentages are 20% or even less (15%) in the Bay of Fundy. This diminished strength of the Sun-caused tides means that the term "spring tide" loses much of its significance. In the Bay of Fundy the varying distance between Earth and Moon is the most important factor in determining tidal strength. Perigean spring tides are outstanding, while apogean spring tides hardly differ from average tides. Thus, the importance otherwise given to the term "spring tide" shows that tidal phenomena around the North American continent are not very well understood in legal circles.
Thirdly, the term "neap, or ordinary tide ... which takes place ... twice every twenty-four hours ..." is a very confusing expression. For example, the period of 24 hours is not very precise because in most cases, the tides occur on average twice in a period of 24.84 hours, the lunar day. However, it is the term "neap or ordinary" that presents difficulty with respect to definition.
The term "High Water of Ordinary Spring Tides" is used in some British publications. The U.S. Coast and Geodetic Survey Tide and Current Glossary (1999) mentions that the term "ordinary" is not used in a technical sense by the Survey, but that term, when applied to the tides may be taken as equivalent to the terms "mean" and "average" (ASCE 1962). Thus, from that service's point of view the "ordinary tide" would be the same as the "mean tide". However a neap tide is a tide weaker than a mean or average tide. Thus the term "... the neap or ordinary tide ..." is a contradiction in terms.
Tide type #3 is correct insofar as this tide takes place between full moon and the "change of the Moon" (new moon), and presumably is the weakest possible. However, the term "ordinary", has various meanings, one being "of common or everyday occurrence", another being "average or mean" (La Forest 1972). However, when a condition is variable, it is not possible for that condition to also happen all the time, yet be the average condition. It is also true that all tides equal to or greater than the neap tide will attain a certain common level. It could be argued that a neap tide is an ordinary tide. However, it certainly will not be a mediocre, medium, mean, normal, or average tide. In this case the weakest possible tide is set as a standard. No mention is made of the variability of the distance between the Moon and Earth although this is an influential cause of tidal variability, and of high tides, and can equal or exceed the effect of the changing phases of the Moon.
In order for true diurnal tide conditions to exist, the amplitude of the diurnal tide must be two to four times larger than the semidiurnal tide, depending on the time relationship between the two. However, under certain astronomical and oceanographic conditions, tides may vary from diurnal to semidiurnal during a span of little over a day. Thus only one tidal oscillation sometimes occurs in the southern parts of the Gulf of St. Lawrence and in Northumberland Strait. This is due to an extreme case of diurnal inequality when the Moon has the greatest degree of declination and the local semidiurnal components of the tide are weak. As the Moon is in its greatest declination when the Sun is near the solstices, diurnal inequalities are the most prominent during the summer and winter months. Another expression of tidal diurnal inequality, prevalent in the Bay of Fundy (Desplanque and Mossman 1998a) is the sequence of Higher High Water-Lower Low Water-Lower High Water-Higher Low Water (see section 5.3.3). This sequence can also be reversed. Other conditions are two High Waters of equal elevations, and two unequal Low Waters (for example, Northumberland Strait) and of two equal Low Waters, but unequal High Waters as observed along the eastern shore of New Brunswick and the north shore of Prince Edward Island. These types of tides are evidently not recognized in legal circles.
12.5. DE JURE MARIS
Clearly the three types of tides, recognized by law, make little sense and can cause a great deal of confusion when applied in court decisions. The delineation and demarcation of boundaries in tidal zones becomes an impossible task when the courts assume conditions which are non-existent. Furthermore, the relative submergence or emergence of the landmass with respect to mean sea level is usually completely overlooked when decisions are made. Coastlines along the Bay of Fundy and southern Nova Scotia are generally submerging more rapidly than the global rise of sea level indicates (Shaw and Forbes 1990). Thus, MSL and also the high tide levels are rising at rates that vary 2 or 3 mm/yr to rates exceeding 8 mm/yr, as claimed for some coastal areas of Maine (Scott and Medioli 1979). In areas where beaches have a very gentle slope, such a rise can make a large annual horizontal shift of the High Water mark. Here the establishment of a permanent property boundary, based on the Mean High Water mark, is totally unrealistic.
The definition of the private-state boundary in common-law countries has its genesis in a 17th Century treatise, "De Jure Maris", by Sir Mathew Hale, chief justice of King's Bench, the highest court in England (Hale 1667). He devised the definitions of the three types of tides discussed above. Sir Mathew wrote his treatise in the same year that the 24-year old Isaac Newton conceived the idea of universal gravitation. At the time, Hale was the chief baron of the exchequer, and probably not yet knowledgeable of the new tidal theories that would follow from Newton's work.
Hale's private studies included investigations in classical law, history, the sciences and theology. He exercised considerable influence on subsequent legal thought. Small wonder, therefore, that his misconceptions on the nature of tides endure. A leading case in point was the precedent set in 1854 by the British decision "Attorney-General vs. Chambers". The facts of the case are not significant but the legal interpretation of tidal terms is particularly important for the Maritime Provinces of Canada. The court was asked to determine the legal rights of the parties, a matter which depended entirely upon the interpretation of the term "high water mark". In its decision the Court emphasized the significance of Hale's doctrine, noting that: "All the authorities concur in the conclusion that the right is confined to what is covered by "ordinary tides", whatever be the right interpretation of that word."
It is clear that the Lord Chancellor had problems with the term "ordinary". The Court defined the ordinary tides as: "... the medium tide between springs and neaps ... It is true of the limit of the shore reached by these tides that it is more frequently reached and covered by the tide than left uncovered by it. For about three days it is left short, and on one day it is reached. This point of the shore therefore is about four days in every week, i.e. for most part of the year reached and covered by the tides ... The average of the medium tides in each quarter of a lunar revolution during the year gives the limit of all usage, to the rights of the Crown on the seashore."
In other words, the High Water mark is calculated by averaging the medium high tide marks for each week in the lunar cycle during the year. It is clear that long term cycles such as an 18-year cycle, were not taken into consideration. Reference to Table 28 shows that this can result in different interpretations of the position of the High Water mark, depending on what year is taken into consideration.
12.6. BOUNDARY ISSUES
In common law, private ownership of land ends at the mean high water mark, and title to the area between the MHW and low water marks (so-called tidelands) is held by the sovereign states. In a leading U.S. Federal case, the United States Supreme Court referred to: "the mean high tide line which is neither the spring tide nor the neap tide, but the mean of all the high tides." Unfortunately, in other cases a different line is used, for example the vegetation line, the highest winter tide, and the mean higher high tide; a few states use the low water line as boundary (Bostwick and Ketchum 1972). Quite apart from the choice of tidal cycle, this lack of standardization bedevils tidal boundary issues on national and international scales. A long-term cycle was taken into account in the U.S.A. in the so-called "Borax" decision (United Sates Supreme Court 1935). In this landmark case in 1935, the United States Supreme Court ruled that "an average 18.6 years of tidal observations should be used to determine the datum elevation". Promoted in the U.S.A., this has been described as a progressive decision which incorporates the most accurate methodology for determining tidal boundaries. However the definition does not deal with submergence of the landmass in relation to mean sea level, difficulties in areas with diurnal or strongly mixed diurnal and semidiurnal tides, and non-tidal influences. Furthermore the 18.6 year cycle is based on the period of revolution of the Moon's nodes and during this period the diurnal inequality of the tides varies in strength.
The 1949 "Tide and Current Glossary" prepared for the U.S. Coast and Geodetic Survey defines MHW as "the average height of the high water over a 19-year period". For shorter periods of observation, corrections are applied to eliminate known variations and reduce the result to the equivalent of a mean 19-year value. The 19-year cycle, the so-called "Metonic Cycle", was chosen because 235 lunations occur almost exactly in 19 mean solar years, and this is in step with the Julian calendar (Greulich 1979). Named for its discoverer, the Greek astronomer Meton (432 B.C.), this cycle was used by the Nicene Council in 325 A.D. to fix the date of Easter.
Unfortunately, in legal cases where tidal heights are important, the emphasis placed on cycles of 18.61 (and 19 years) may not be warranted. This is the case in regions like the Bay of Fundy where diurnal inequality of the tides is of such minor importance that it can be virtually ignored among variations caused by the coincidence of perigean and spring tides. Table 22 shows the situation with respect to long term cycles of conditions leading to stronger and weaker than normal tides. Note that if one used 246 anomalistic months (18.558 years), 247 anomalistic months (18.634 years), or 252 anomalistic months (19.011 years), the multiples of other types of months are not nearly as closely matched as with 18.03 years. Thus, the courts may easily be led astray by misapplying astronomical data.
In theory, the height reached at High Water is the full amplitude above MSL, which is defined as the level that oceanic water would assume if no tidal or atmospheric influences are acting upon it. 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 this was adjusted in the Canadian levelling network. Because in most areas of the Maritime Provinces the landmass is submerging relative to MSL, geodetic datum drops gradually below Mean Sea Level. Thus, local MSL at present is about 280 mm (0.9 ft) higher than G.D. However, there is a dearth of data, and no one is certain what the exact 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 and it is no less likely to trouble legal minds.
12.7. DETERMINATION OF MHW, BAY OF FUNDY
A legal decision regarding tidal issues in the Bay of Fundy resulted from the 1962 to 1965 trial proceedings in the case of Irving Limited and the Municipality of the County of Saint John vs. Eastern Trust Company. This trial (for details see Desplanque and Mossman 1999a) highlighted a wholesale incorrect use of tidal data and definitions. Central to this case was the definition of Mean High Water (MHW). In brief, it transpires that no matter what is chosen as a MHW elevation, the value employed in the Irving case has no valid statistical basis.
In retrospect, it is instructive to consider the manner in which MHW (and HHW) vary according to the increased tidal range toward the head of the Bay of Fundy. This will be illustrated for the Minas Basin, where seven principal tidal constituents account for more than 90% of the total variability of the tides (see Table 3). Note that while the amplitudes of these semidiurnal tides increase toward the head of the Bay and Basin, the diurnal amplitudes remain virtually constant at 0.2 meters. The shallow-water tides are relatively small, but will certainly become large for locations within estuaries. No constituents are available for the tides within the estuaries. However the diurnal tides probably will not be altered when progressing into the estuaries. Semidiurnal amplitudes are clearly a function of the distance from the port of Saint John where the principal tidal hydrographic station is located. Thus as shown in section 5.3.2, the range of the dominant semidiurnal tides in the Bay of Fundy increases exponentially as they advance, at the rate of about 0.36% per kilometre. This allows local tidal range to be estimated very accurately, with reference to Geodetic Datum, from which follow realistic estimates of MWL and HHW.
The above relationship is, among other things, relevant to proposed tidal power schemes in the Bay of Fundy. These might very well modify the tidal regime (Greenberg 1987) and conceivably lead to international legal conflicts. Indeed a model used during the 1977 studies for Fundy tidal power development concluded that should a tidal power plant be built in the Minas Basin, the amplitude of average tides would increase by 0.15 m along the Gulf of Maine coastline of New England, and up to 0.25 m along New Brunswick coastline. Whatever the truth of this dire prediction, the fact is that coastal submergence is a reality that must be faced due to continuing sea-level rise. No protest, political or otherwise, can alter this situation. Further, if MHW is to be established, one has to make the choice between a permanent level linked to a certain year such as the Geodetic Datum of Canada, or a level which moves with changes in sea level due to geomorphological influences triggered by eustatic sea-level rise.
When the International Court of Justice set the boundary line between Canada and the United States through the Gulf of Maine, in October 1984, people on both sides of the border protested that the Court had decreased the area of the Gulf of Maine to such a degree that many jobs would be lost in both countries. If that same Court has to make a decision about changing characteristics of the tides and water levels in the Gulf of Maine-Bay of Fundy system, our knowledge of these characteristics had better be able to stand up to close examination.
12.8. THE BOTTOM LINE
An interdisciplinary approach is needed in the matter of tidal boundary delimitation. However, whatever the roles of lawyers, surveyors and scientists, the terms MHW and MLW need to be unambiguously defined in accordance with modern tidal and astronomical principles and terminology. European tidal conditions taken as standard in legal circles are not universal and consequently do not permit recognition of various common types of tides such as those governed by diurnal inequalities. Establishment of tidal boundaries is impossible when courts assume non-existent conditions.
Tidal datums are commonly misconceived to be fixed planar levels rather than undulating time and space-dependent surfaces. Yet, except for non-astronomical factors such as storm surges, tectonic activity and postglacial sea-level rise, tidal prediction with reference to specific tide levels can be made with a high degree of confidence. In fact there is a tendency to give greater credence to the predictions and the tidal constituents on which they are based than to the observed tides. However, if the procedure is correct, the average of the predicted and observed heights should be close together. The more accurate establishment of tidal datums hinges on improved prediction, which in turn requires more reference ports, updated tidal information and improved surveying techniques. Where numerous ports exist as along the eastern Canadian seaboard and the M2 tidal constituent is dominant, the amplitude of the [M.sub.2] tide as measured above local MSL, closely approaches MHW. Also, the exponential increase in amplitude of the semidiurnal tides in the Bay of Fundy allows MWL, HHW and the local tidal ranges to be predicted quite accurately in this home to the world's highest tides.
Table 25. Comparison of Canadian and American Tide Tables (1975) of tidal ranges for the same six selected ports Canadian Tables U.S. Tables Large Sping (All units in feet) Mean Tides Mean Tides [M.sub.2] Saint John, NB 21.9 30.0 20.8 23.7 10.09 Burntcoat Head, NS 39.1 52.6 38.4 43.5 18.51 Halifax, NS 4.7 6.9 4.4 5.3 2.07 North Sydney, NS 3.1 4.7 2.6 3.2 1.23 Pictou, NS 4.0 6.4 3.2 3.9 1.40 Charlottetown, PEI 6.0 9.6 5.2 6.4 2.33 Notes. Values for [M.sub.2] tidal constituent are taken from "Harmonic Constants and Associated Data" of the Canadian Marine Sciences Branch, 1969. Table 26. Mean tide levels at several Atlantic Canada ports illustrating the contribution of semidiurnal and diurnal constituents Mean Tide Level Mean Tide Level above local Chart above Mean Water Datum Level (All units in feet) HHW LHW MHW HHW LHW MHW Saint John, N.B. 25.1 24.2 14.3 10.8 9.9 10.35 Yarmouth, N.S. 13.8 13.0 7.9 5.9 5.1 5.5 Halifax, N.S. 6.4 6.0 4.1 2.3 1.9 2.1 North Sydney, N.S. 4.6 4.2 3.1 1.5 1.1 1.3 St. John's, Nfld. 4.0 3.4 2.5 1.5 0.9 1.2 Pictou, N.S. 5.6 4.9 3.7 1.9 1.2 1.55 Charlottetown, P.E.I. 8.0 7.4 5.3 2.7 2.1 2.4 Shediac Bay, N.B. 3.9 3.4 2.8 1.1 0.6 0.85 Rustico, P.E.I. 2.9 1.5 1.6 1.3 -0.1 0.6 Pointe St. Pierre, Que. 4.3 2.8 2.4 1.9 0.4 1.15 Tidal Constituent (All units in feet) [M.sub.2] [K.sub.1] Saint John, N.B. 10.09 0.50 Yarmouth, N.S. 5.35 Halifax, N.S. 2.07 0.34 North Sydney, N.S. 1.23 St. John's, Nfld. 1.16 0.25 Pictou, N.S. 1.40 0.68 Charlottetown, P.E.I. 2.33 0.84 Shediac Bay, N.B. 0.65 0.84 Rustico, P.E.I. 0.55 0.60 Pointe St. Pierre, Que. 1.16 0.63 Notes. At ports where the semidiurnal constituent [M.sub.2] is dominant, the height of MHW is only a few hundreds to a few tenths of a foot higher than the height of [M.sub.2] above that level. Where the diurnal tide [K.sub.1] is dominant, as in Shediac Bay, N.B., and Rustico, P.E.I., this constituent governs the mean tide height. (Data from v. 1 and 2 of Canadian Tide and Current Tables for the Atlantic Coast, Bay of Fundy and Gulf of Saint Lawrence and the 1979 Manual of the Tides and Water Levels Section of the Canadian Hydrographic Service) Table 27. Highest monthly tides at ports along eastern and western coastlines of North America, and the eastern side of the North Atlantic Ocean in 1953 and 1975 Year J F M A M J Lisbon, Portugal 1953 1.80 1.95 1.98 1.89 1.74 1.65 1975 1.95 2.01 1.95 1.83 1.71 1.65 Liverpool, England 1953 4.33 4.63 4.57 4.30 3.72 3.75 1975 4.94 5.03 4.88 4.48 4.18 4.08 Halifax, Canada 1953 0.98 0.98 1.01 0.94 0.91 0.82 1975 1.07 1.07 1.04 0.98 0.88 0.85 Saint John, Canada 1953 3.99 4.27 4.33 4.30 4.05 3.72 1975 4.18 4.30 4.30 4.33 4.08 3.78 New York, U.S.A. 1953 0.94 0.94 1.01 1.07 1.10 1.04 1975 1.01 0.98 1.07 1.13 1.10 1.04 Vancouver, Canada 1953 1.83 1.71 1.52 1.43 1.52 1.62 1975 2.04 1.89 1.74 1.55 1.62 1.80 San Francisco, U.S.A. 1953 1.07 1.01 0.88 0.94 1.01 1.04 1975 1.07 0.98 0.91 0.98 1.01 1.04 Year J A S O N D Lisbon, Portugal 1953 1.86 2.01 2.04 1.95 1.80 1.74 1975 1.71 1.92 2.07 2.10 1.95 1.92 Liverpool, England 1953 4.21 4.60 4.60 4.33 3.81 3.57 1975 4.51 4.88 5.03 4.69 4.72 4.42 Halifax, Canada 1953 0.85 0.94 1.01 1.10 1.04 0.94 1975 0.88 0.94 1.01 1.07 1.07 1.04 Saint John, Canada 1953 3.99 4.15 4.30 4.36 4.15 3.81 1975 3.96 4.18 4.30 4.42 4.39 4.18 New York, U.S.A. 1953 1.07 1.10 1.13 1.16 1.07 0.94 1975 1.07 1.13 1.13 1.19 1.16 1.07 Vancouver, Canada 1953 1.62 1.52 1.43 1.31 1.52 1.62 1975 1.86 1.80 1.71 1.55 1.68 1.74 San Francisco, U.S.A. 1953 1.04 0.98 0.94 1.04 1.10 1.10 1975 1.01 1.04 0.94 1.01 1.07 1.10 Notes. Heights in metres above mean water level. Note that highest tides are not necessarily equinoctial. (After Desplanque and Mossman, 1998a) Table 28. Height (in feet from local Chart Datum) of the largest predicted tides for each month from 1927 to the end of 1997 for the port of Saint John, New Brunswick Jan. Feb. Mar. Apr. May June 1927 26.2 26.9 27.6 28.2 28.4 27.6 1928 26.4 27.5 28.4 (28.6) 28.1 27.6 1929 26.5 25.8 25.5 26.6 27.5 (27.7) 1930 FM 26.7 26.7 26.6 26.5 25.9 26.3 1931 26.4 27.1 27.4 27.7 27.8 25.9 1932 26.2 27.0 27.8 (28.2) 28.0 27.1 1933 26.4 25.8 27.0 27.7 (28.0) 27.9 1934 27.4 27.1 26.7 26.6 27.1 27.4 1935 NM 27.8 28.1 28.1 28.2 27.8 27.0 1936 27.4 27.7 28.3 28.3 27.8 27.1 1937 26.5 26.7 27.7 28.4 (28.6) 28.3 1938 27.9 27.3 26.5 26.9 28 (28.2) 1939 FM 28.2 28.3 28.1 28.0 27.3 27.9 1940 28.0 28.2 (28.9) 28.6 28 26.1 1941 26.8 27.6 28.2 (28.2) (28.9) 28.2 1942 27.7 26.9 26.5 27.6 (28.7) 28.1 1943 NM (28.1) 27.9 27.3 26.9 27.2 27.8 1944 28.0 28.1 28.0 27.7 27.1 26.1 1945 26.8 27.7 28.1 28.3 28.6 27.8 1946 26.0 26.0 26.9 27.9 (28.3) (28.3) 1947 FM (27.8) 27.1 26.8 27.0 (27.8) (27.8) 1948 (27.6) 27 27.3 27.1 26.4 26.3 1949 26.9 27.6 28.0 (28.4) 27.9 26.9 1950 26.0 26.5 27.3 28.2 (28.5) 28.0 1951 27.3 26.8 26.9 27.4 (27.6) 27.5 1952 NM (27.9) 27.6 27.1 26.9 26.4 27.0 1953 27.6 28.2 28.4 28.3 27.5 26.4 1954 26.1 27.2 28.0 28.7 (28.8) 27.8 1955 27.3 26.7 27.7 28.4 (28.5) 28.1 1956 FM 28.0 27.5 26.9 26.9 27.6 28.1 1957 28.4 (28.5) 28.3 28.0 27.1 27.5 1958 27.3 28.1 28.7 (29.1) 28.9 28.0 1959 26.6 27.5 28.6 28.7 (29.0) 28.4 1960 27.9 27.2 26.6 27.8 28.4 (28.61) 1961 NM (28.6) 28.5 28.0 27.5 26.8 27.9 1962 27.7 28.5 (28.8) 28.4 28.3 27.3 1963 27.0 27.9 28.4 (29.0) 28.6 27.7 1964 27.7 27.0 27.5 28.4 (28.9) 28.8 1965 FM (28.6) 28.2 27.6 27.1 27.5 28.2 1966 28.3 28.8 (28.9) 28.6 28.1 27.1 1967 27.0 27.7 28.2 28.4 27.9 26.9 1968 26.2 26.4 27.3 (28.0) 27.9 27.6 1969 NM (27.9) 27.5 26.6 26.9 27.4 27.6 1970 28.2 (28.5) 28.2 27.5 26.9 26.7 1971 28.2 28.7 (28.8) 28.4 27.6 26.3 1972 27.2 27.3 28.1 28.7 (28.8) 28.2 1973 27.3 26.6 27.2 28.0 (28.4) (28.4) 1974 FM (28.4) 28.1 27.7 27.1 27.5 27.9 1975 27.9 28.3 28.3 28.4 27.6 26.6 1976 26.8 27.5 27.5 (29.0) 28.9 28.2 1977 27.3 26.5 27.1 28.1 28.9 (29.1) 1978 27.9 27.1 27.1 27.9 (28.4) 28.3 1979 NM (28.1) 27.7 27.2 27.1 27.3 27.9 1980 27.2 27.8 28.1 (28.4) 28.2 27.6 1981 27.2 26.8 27.3 27.8 (28.2) 28.1 1982 FM (27.8) 27.4 27.0 27.3 27.7 27.5 1983 27.6 (27.7) 27.4 27.3 27.0 26.7 1984 27.2 27.8 28.0 28.1 27.8 26.6 1985 26.4 27.0 27.4 27.9 (28.0) 27.5 1986 27.0 26.7 27.1 (27.4) (27.4) 27.0 1987 NM (27.4) 27.3 26.8 26.8 26.4 26.5 1988 27.3 (27.8) 27.6 27.7 27.3 26.4 1989 26.5 27.3 27.7 (28.0) 27.9 27.1 1990 26.8 26.7 27.4 (27.6) 27.4 27.0 1991 FM (27.5) 27.4 27.3 26.7 26.9 27.1 1992 27.8 (28.0) 27.8 27.6 27.0 26.6 1993 27.2 27.8 28.0 (28.3) 27.9 27.2 1994 27.0 27.3 28.0 (28.2) 27.9 27.4 1995 27.8 27.6 27.2 27.5 27.8 27.8 1996 NM (28.1) (28.1) 27.7 27.4 27.0 27.3 1997 27.6 (28.2) (28.2) 28.1 27.9 27.4 July Aug. Sep. Oct. Nov. Dec. 1927 26 26.7 27.4 28.2 28.5 27.9 1928 27.6 26.1 26.5 28.2 28.4 27.9 1929 27.5 27.0 26.5 26.5 27.0 27.2 1930 FM 26.7 (27.0) (27.0) 26.9 26.2 25.3 1931 26.6 27.3 27.6 (28.0) 27.7 26.9 1932 26.2 26.1 26.8 27.0 27.7 26.8 1933 27.1 26.9 26.4 27.1 27.7 27.8 1934 (27.7) 27.4 27.1 27.0 26.1 26.9 1935 NM 27.7 28.2 28.4 (28.6) 28.0 27.0 1936 26.2 27.0 27.6 (28.6) 28.0 27.2 1937 27.4 26.9 27.1 28.0 28.4 28.3 1938 28.0 27.5 27.0 26.9 27.2 28.0 1939 FM 28.2 (28.5) 28.3 28.2 27.8 27.3 1940 26.9 27.6 28.1 (28.8) 28.2 27.1 1941 27.4 27.9 27.9 27.9 28.8 28.4 1942 27.9 27.0 26.2 27.0 27.0 28.2 1943 NM 27.9 27.9 27.8 27.3 26.9 27.4 1944 27.3 27.8 28.0 28.1 (28.2) 27.1 1945 26.8 27.2 27.9 (28.7) 28.6 27.9 1946 27.4 26.1 26.1 27.1 28.0 28.1 1947 FM 27.6 27.1 26.9 26.5 26.0 27.0 1948 26.9 27.4 (27.6) (27.6) 27.5 26.6 1949 26.5 27.4 28.0 (28.4) 28.0 27.0 1950 27.1 25.6 26.8 27.9 28.2 28.0 1951 27.4 27.0 26.5 26.8 27.4 27.6 1952 NM 27.5 27-8 27.8 27.8 27.2 26.6 1953 27.3 27.8 28.3 (28.5) 27.8 26.7 1954 25.9 26.7 27.7 28.4 28.6 28.0 1955 27.5 26.5 26.1 27.0 28.2 28.4 1956 FM (28.3) 28.2 27.8 27.4 27.1 27.9 1957 28.1 28.4 27.4 27.5 27.3 27.0 1958 26.8 27.6 28.5 (29.1) 29.0 28.3 1959 27.5 26.6 26.9 28.0 28.8 (29.0) 1960 28.5 28.0 27.4 26.9 27.8 28.4 1961 NM 28.3 28.3 28.0 27.7 27.1 26.9 1962 27.3 28.0 28.4 28.6 28.5 27.6 1963 26.7 26.4 27.3 28.1 28.7 28.6 1964 28.2 27.7 27.2 27.9 28.5 28.6 1965 FM 28.4 28.3 26.9 27.5 26.9 27.5 1966 27.8 28.4 28.7 (28.9) 28.4 27.4 1967 25.6 26.4 27.4 28.3 (28.6) 28.2 1968 26.8 26.3 26.5 27.8 27.9 27.7 1969 NM 27.5 27.1 26.5 26.3 26.8 27.5 1970 27.4 27.8 27.7 27.9 27.4 27.1 1971 26.2 27.1 27.9 28.5 (28.8) 28.1 1972 27.4 26.5 27.5 28.2 28.6 28.5 1973 27.4 26.8 26.5 27.3 28.1 (28.4) 1974 FM 28.2 28.1 28.0 27.7 27.1 28.0 1975 27.2 27.9 28.3 (28.7) 28.6 27.9 1976 27.2 27.2 28.0 28.8 28.8 28.3 1977 28.4 27.1 26.4 27.7 28.2 28.6 1978 27.8 27.2 26.6 26.5 27.5 28.1 1979 NM (28.1) 28.0 27.7 27.7 27.5 27.1 1980 26.8 27.3 27.6 28.3 28.3 27.9 1981 27.5 27.0 26.7 27.6 27.8 27.9 1982 FM 27.3 27.3 27.0 26.9 26.8 27.4 1983 27.0 27.5 27.6 27.6 27.5 27.2 1984 26.7 27.3 27.8 (28.1) 27.9 27.1 1985 26.8 26.4 27.0 27.6 27.8 27.2 1986 26.9 26.7 26.4 26.4 26.9 26.9 1987 NM 26.9 27.3 27.2 27.2 27.0 26.6 1988 27.0 27.4 27.7 27.7 27.3 26.5 1989 26.2 26.7 27.4 27.8 27.6 27.1 1990 26.8 26.6 26.2 26.9 27.2 27.2 1991 FM 27.4 (27.5) 27.2 27.2 26.8 27.2 1992 27.4 27.7 27.9 27.8 27.2 26.5 1993 26.8 27.2 27.8 28.1 27.9 27.4 1994 27.0 26.6 26.8 27.5 27.9 27.9 1995 27.8 27.6 27.2 27.0 27.5 (27.9) 1996 NM 27.6 27.9 27.8 27.7 27.3 27.1 1997 27.2 27.7 27.9 28.2 28.1 27.6 Next Saros Year cycle year 1927 28.5 (1945) 1928 FM 28.6 (1946) 1929 27.7 (1947) 1930 27.0 (1948) 1931 28.0 (1949) 1932 28.2 (1250) 1933 NM 28.0 (1951) 1934 27.7 (1952) 1935 28.6 (1953) 1936 28.6 (1954) 1937 FM 28.6 (1955) 1938 28.2 (1956) 1939 28.5 (1957) 1940 28.8 (1958) 1941 NM 28.9 (1959) 11 May 1942 28.7 (1960) 1943 28.1 (1961) 1944 28.2 (1962) 1945 28.7 (1963) 1946 FM 28.3 (1964) 1947 27.8 (1965) 1948 27.6 (1966) 1949 28.4 (1967) 1950 NM 28.5 (1968) 1951 27.6 (1969) 1952 27.9 (1970) 1953 28.5 (1971) 1954 28.8 (1472) 1955 FM 28.5 (1973) 1956 28.3 (1974) 1957 28.5 (1975) 1958 29.1 (1976) 10 April 1959 NM 29.0 (1977) 22/24 May 1960 28.6 (1978) 1961 28.6 (1979) 1962 28.8 (1980) 1963 29.0 (1981) 1964 FM 28.9 (1982) 1965 28.6 (1983) 1966 28.9 (1984) 1967 28.6 (1985) 1968 28.0 (1986) 1969 NM 27.9 (1987) 1970 28.5 (1988) 1971 28.8 (1989) 1972 28.8 (1990) 1973 FM 28.4 (1991) 1974 28.4 (1992) 1975 28.7 (1993) 1976 29.0 (1994) 16 April 1977 NM 29.1 (1995) 3 June 1978 28.4 (1996) 1979 28.1 (1997) 1980 28.4 (1998) 1981 FM 28.2 (1999) 1982 27.8 (2000) 1983 27.7 (2001) 1984 28.1 (2002) 1985 28.0 (2003) 1986 NM 27.4 (2004) 1987 27.4 (2005) 1988 27.8 (2006) 1989 28.0 (2007) 1990 FM 27.6 (2008) 1991 27.5 (2009) 1992 28.0 (2010) 1993 28.3 (2011) 1994 NM 28.2 (2012) 27 April 1995 27.9 (2013) 13/15 June 1996 28.1 (2014) 1997 28.2 (2015) Notes. For each year the highest monthly tide within a 7-month cycle is underlined, likewise the highest annual tides (underlined in the second last column) that occur in each 4 - 5 year cycle. In each case the corresponding year of the next Saros is given in brackets (last column). Since one of the 7-month cycles is related to the full moon coincident with perigee, and the other 7-month cycle with the new moon coincident with perigee, the cycles are marked with FM or NM respectively. Highest tide of the year in brackets.
The hydrodynamic vigour of the Bay of Fundy rules over such geologically significant processes as erosion, sediment dynamics, and the Bay's natural resources and ecosystems. However, there is a clear need to more exactly evaluate the dynamics of the tidal regime in order to better understand the multitude of geological processes at work. Conclusions from investigations to date are summarized below.
1) Along the eastern Canadian seaboard the [M.sub.2] tidal constituent is dominant and the amplitude of the [M.sub.2] tide as measured above MSL closely approaches MHW. MSL and MHW are rising in respect to the land at an average rate of 2 to 3 mm/year.
2) As they advance toward the head of the Bay of Fundy, tidal ranges commonly exceed 15 m, and the amplitude of the dominant semidiurnal tides increases exponentially at the rate of 0.36 %/ km. This allows the local tidal range to be predicted very accurately, likewise MWL and HHW.
3) An integral part of the western North Atlantic Ocean, the Bay of Fundy tides hydrodynamically exhibit the effects of a co-oscillating tide superimposed upon the direct astronomical tide.
4) Forcing by the North Atlantic tide drives Bay of Fundy tides primarily by standing wave conditions developed through resonance; differences in the tidal range through the Bay of Fundy-Gulf of Maine-Georges Bank System are, in effect, governed by the rocking of a tremendous seiche.
5) Although dominantly semidiurnal, Fundy tides nevertheless experience marked diurnal inequalities. The 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 extra high tides.
6) Extra-high tides can occur at all seasons in the Bay of Fundy, depending on the year in question. The result is considerable tidal variation throughout the year. Distinct cycles of 12.4 hours, 24.8 hours, 14.8 days, 206 days, 4.53 years, and 18.03 years are recognized.
7) Three main astronomical tide-generating factors determine the number of tides that can exceed a certain elevation during any given year: the variable distance between the Earth and the Moon; the variable positions of the Moon, Sun, and Earth relative to each other; the declination of the Moon and Sun relative to the Earth's equator.
8) Vigorous interplays between land and sea occur in northern macrotidal regimes. In Bay of Fundy estuaries, the rising sea level continually re-establishes salt marshes at higher levels despite infrequent floodings.
9) The largest tides arrive in sets of 7 months, 4.53 years and 18.03 years, and most salt marshes are built up to the level of the average tide of the 18 year cycle. Assuming local marsh level to be 1.2 m beneath the high water level of extreme high tides, an empirical High Marsh Curve allows the number of annual floodings to be determined.
10) Marigrams constructed for estuaries of rivers feeding into the Bay of Fundy show the tidal wave progressively reshaped over its course, and that its sediment-carrying and erosional capacities vary as a consequence of changing water surface gradients.
11) Changing seasons effect substantial alterations in the character of estuaries. Thus winter contributes to an already complex tidal regime, especially during the second half of the 7-month cycle. Heaviest ice conditions occur one or two months before perigean and spring tides combine to form the largest tide of the cycle. At this time, the difference in height between neap tide and spring tide is increasing, resulting in the optimal time for flooding of marshlands.
12) Changing environmental conditions in the Bay of Fundy may signal an increase in the dynamic energy of the tides. Observations indicate critical connections between tides, currents, erosion, sedimentation, and the biological community. There is a clear need to more precisely evaluate the dynamics of the tidal regime and to better understand the myriad geological processes at work.
We are pleased to acknowledge that selected source materials for this work derived from the Maritime Marshlands Rehabilitation Administration (MMRA) observations (1950-1965), and from Maritime Resource Management Services (MRMS) archives (1972-1987), Amherst, Nova Scotia. This research has been facilitated by a grant in aid of research (#A8295) to DJM from the Natural Sciences and Engineering Research Council of Canada. We are likewise grateful to Mount Allison University for financial and logistical assistance. Helpful advice and friendly discussions have been generously contributed by individuals at the Bedford Institute of Oceanography, Dartmouth, Nova Scotia: J. Shaw, A.C. Grant, G. Fader, R.B. Taylor and D. Frobel of Geological Survey of Canada (Atlantic), Natural Resources Canada; and C.T. O'Reilly, B. Petrie and D. Greenberg of Fisheries and Oceans Canada. Special thanks to journal referees J. Shaw and C. Hannah for their important productive criticism. The advice of G.N. Ewing, former Dominion Hydrographer, on regional tides is greatly appreciated, likewise that of D.L. DeWolfe, formerly of the Canadian Hydrographic Service, on North Atlantic tides. P. Cant, Sackville, N.B. kindly provided valuable advice on extensive portions of an early draft of this paper. Early collaborations by the senior author with C.L. Amos (formerly of GSCA), D.C. Gordon (DFO) and D.I. Bray (University of New Brunswick) are freely acknowledged. D. Estabrooks and A. Estabrooks competently assisted with typing, formatting and layout. We are especially appreciative, too, of the extensive constructive editorial advice received from R.A. Fensome (Geological Survey of Canada, Atlantic) during the final pre-publication period. Reproduction of certain portions of our previously published material has been generously permitted by Geoscience Canada, Atlantic Geology and The Geographical Review, and for this we are grateful.
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Editorial responsibility: Robert A. Fensome
Appendix Glossary of Terms
Aboiteau. Gated drainage sluice built into a dyke.
Amphidromic point. A point of zero amplitude of the observed or constituent tide.
Amphidromic system. A region surrounding an amphidromic point from which radiating cotidal lines progress through all hours of the tidal cycle.
Amplitude. Half the height or range of the wave, and the distance that the tide moves up or down from Mean Water Level.
Anomalistic cycle (monthly). Cycle in the average period (27.555 days) of the revolution of the Moon around Earth with respect to lunar perigee.
Aphelion. The point in Earth's orbit farthest from the Sun.
Apogean tide. Tide of decreased range occurring monthly when the Moon is in apogee.
Apogee. The point on the Moon's orbit that is farthest from Earth.
Argument. The angle indicated by the cosine term in an equation describing harmonic motion.
Astronomical tide (gravitational tide, equilibrium tide). The theoretical tide formed assuming that waters covering the face of the Earth instantly respond to the tide-producing forces of the Moon and Sun and form a surface of equilibrium under the action of these forces.
Barycentre. The combined centre of mass around which Earth and Moon revolve in essentially circular orbits.
CD. See "chart datum".
Celerity (of a wave). The speed or horizontal rate of advance of a wave.
Centrifugal force. Outward directed force acting on a body moving along a curved path or rotating about an axis.
Centripetal force. A centre-seeking force that tends to make rotating bodies move toward centre of rotation.
Chart datum (CD). An established elevation so low that the tides at that place will seldom if ever fall below it.
Constituents. The cosine terms in an equation describing tidal harmonic motion.
Continental shelf. Zone extending from the line of permanent immersion to the depth (average 130 m) where a steep descent occurs to great depths.
Coriolis effect. Also known as Coriolis force. An apparent force acting on a body in motion, due to rotation of the Earth causing deflection to the right in northern hemisphere and to the left in southern hemisphere.
Cotidal lines. Lines on a map giving the location of the tide's crest at stated time intervals.
Crest of a wave. Highest part of a propagating wave.
Current. A horizontal movement of water.
Declination. The angular distance of the Moon or Sun above or below the celestial equator.
Diurnal. Daily tides; having a period or cycle of approximately one tidal day.
Diurnal inequality. The difference in height between the two High Waters or the two Low Waters of each tidal day.
Drumlin. A streamlined hill of compact glacial fill formed by a glacier.
Dynamic tidal theory. Model of tides that takes into account the effects of finite ocean depth, basin resonances and the presence of continents.
Ecliptic. The plane of the centre of the Earth-Moon system as it orbits around the Sun; the intersection of the plane of Earth's orbit with the celestial sphere.
Equal High Water (EHW). Two daily high tides of equal height.
Equal Low Water (EHW). Two daily low tides of equal height.
Equilibrium theory. See "astronomical tide".
Equilibrium tide. Hypothetical tide due to the tide-producing forces under the equilibrium theory; also known as the gravitational tide.
Equinox. Times of the year when the Sun stands directly above the equator so that day and night are of equal length around the world (about 21 March and 22-23 September).
Estuary. A coastal embayment into which fresh river water enters at its head and mixes with the relatively saline ocean water.
Eustatic. Pertaining to global changes of sea level that affected all oceans as a result of absolute changes in the quantity of sea water.
Evectional (monthly) cycle. The time required for the revolution of Moon around Earth, depending upon the variation of the eccentricity of its orbit.
Exponential (growth). A variable with a constant growth rate is said to increase exponentially.
Forced wave. A wave generated and maintained by a continuous force.
Free wave. A wave that continues to exist after the generating force has ceased acting.
Frequency of wave. The number of cycles that pass a location during a unit of time.
Gravity wave. A wave from which the restoring force is gravity.
Harmonic analysis. The mathematical process by which the observed tide or tidal current at any location is separated into harmonic constituents.
Head. The difference in water level at either end of a strait, channel, etc.
Height (range) of a wave. Vertical distance between wave crest and the adjacent wave troughs.
Higher High Water (HHW). The higher of two daily High Waters.
Higher High Water, large tide (HHWLT). Average of the highest high waters, one from each of 19 years of predictions.
Higher High Water, mean tide (HHWMT). Average of all the high waters from 19 years of predictions.
Higher Low Water (HLW). The higher of two daily Low Waters.
High Water (HW). Maximum height reached by a rising tide as a result of periodic tidal forces and the effects of meteorological, hydrologic and/or oceanographic conditions.
Holocene. The latest epoch of the Cenozoic era, from the end of the Pleistocene epoch to the present time. In northern latitudes, it generally equates with the postglacial interval.
Ice factories. Open water consisting of an unconsolidated mixture of needle-like ice crystals and sediment-laden waters.
Ice walls. Vertical walls of ice up to 5 m high formed in a rectangular estuarine channel under winter conditions.
Intertidal zone. The zone between mean higher high water and mean lower low water lines.
Isostatic compensation. Adjustment of crust of the Earth to maintain equilibrium among units of varying mass and density.
Julian calendar. Introduced by Julius Caesar 45 B.C.E., this calendar provided that the common year should consist of 365 days, and that every fourth year, now known as leap year, should contain 366 days, making the average length of the year 365.25 days. It differs from the modern (Gregorian) calendar in which the calendar century years not divisible by 400 are common years.
[K.sub.1]. Luni solar diurnal constituent; with [O.sub.1] it expresses the effect of the Moon's declination.
[K.sub.2]. Luni solar semidiurnal constituent; it modulates amplitude and frequency of [M.sub.2] and [S.sub.2] for the declinational effect of the Moon and Sun, respectively.
Knot. Speed unit of one nautical mile (1852 metres) per hour.
[L.sub.2]. Smaller lunar elliptic semidiurnal constituent; with [N.sub.2] it modulates the amplitude and frequency of [M.sub.2] for the effect of variation in the Moon's orbital speed due to its elliptical orbit.
Lag (deposit). Larger sedimentary particles remaining after smaller particles are washed away.
Latitude. Angular distance between point on the Earth and the equator measured north or south from the equator along a longitudinal meridian.
Longitude. Angular distance along the equator east and west of Greenwich measured in degrees or hours, the hour being taken as 15[degrees] of longitude.
Lower High Water (LHW). The lower of two daily High Waters.
Lower Low Water (LLW). The lower of two daily Low Waters, or a single Low Water.
Lower Low Water, large tide (LLWLT). Average of lowest low waters, one from each of 19 years of predictions.
Lower Low Water, mean tide (LLWMT). Average of all the lower low waters from 19 years of predictions.
Lowest Normal Tide (LNT). Currently synonymous with LLWLT; it is also called chart datum (CD).
Low Water (LW). Lowest height of the tide in daily cycle.
Lunar day. The time of Earth's rotation with respect to the Moon; mean lunar day = 24.84 solar hours.
Lunar month (synodical month). A period of 29 1/2 days in which the Moon passes through four phases: new moon, first quarter, full moon, and last quarter.
[M.sub.1]. Smaller lunar elliptic diurnal constituent; it helps to modulate the amplitude of the declinational [K.sub.1] for effect of the Moon's elliptical orbit.
[M.sub.2]. Principal lunar semidiurnal constituent; it represents the rotation of Earth with respect to the Moon.
Macrotidal. Tidal system in which the tidal range exceeds 4 m.
Marigram (tidal curve). A graphical record of the rise and fall of the tide.
Mean Higher High Water (MHHW). The average of the Higher High Water height on all tidal days observed during a tidal datum epoch.
Mean High Water mark (MHW). The level reached by the [M.sub.2] amplitude above MSL; in Canada, usually taken as equivalent to "ordinary" high water (OHW).
Mean Low Water (MLW). The average of the Lower Low Water height of all tidal days during the tidal datum epoch.
Mean Lower Low Water (MLLW). The average of the Lower Low Water height on all tidal days observed during a tidal datum epoch.
Mean Sea Level (MSL). The level that oceanic water would assume if no tidal or atmospheric influences are acting upon it.
Mean Water Level (MWL). Average of all hourly water levels with respect to chart datum observed over the available period of record.
Meridian. Circle of longitude passing through the poles and any given point on Earth's surface.
Meterological tides. Tidal constituents having their origin in daily or seasonal variations in weather conditions which may occur with some degree of periodicity. MHW. See Mean High Water mark.
Mixed tide. Tide having a conspicuous diurnal inequality in the Higher High and Lower High Waters and/or Higher Low and Lower Low Waters.
Moraine. Hill or ridge of sediment deposited by glaciers; geomorphologic name for a land form composed mainly of till deposited by either an extant or extinct glacier.
MSL. See Mean Sea Level.
MWL. See Mean Water Level.
[N.sub.2]. Longer lunar elliptic semidiurnal constituent; with [L.sub.2] it modulates the amplitude and frequency of [M.sub.2] for the effect of variation in the Moon's orbital speed.
Neap tide. Tide occurring near the first and last quarter of the moon, when the range of the tide is least.
Nodical month. Average period (27.212 days) of the revolution of the Moon around Earth relative to its passing through the ecliptic.
[O.sub.1]. Lunar diurnal constituent; with [K.sub.1] it expresses the effect of Moon's declination; and with [P.sub.1] it expresses the effect of the Sun's declination.
Ordinary High Water (OHW). In Canada, a level in surveying practice taken as equivalent to Mean High Water.
Outwash (glacial). Stratified detritus washed out from a glacier by melt water streams and deposited beyond the terminal moraine or margin of active glacier.
Overpressure. Excessive pressure.
Overtides. Analogous to overtones in music, and considered as higher harmonics of the fundamental tides.
[P.sub.1]. Solar diurnal constituent; with [K.sub.1] it expresses the effect of the Sun's declination.
Perigean tide. A spring tide occurring monthly when the Moon is at or near perigee of its orbit.
Perigee. The point on the Moon's orbit that is nearest Earth.
Perihelion. The point in Earth's orbit nearest to the Sun.
Period. Interval required for the completion of a recurring event or any specific duration of time.
Phase lag. Angular retardation of a maximum of a constituent of the observed tide behind the corresponding maximum of the same constituent of the equilibrium tide.
Prime meridian. Meridian of longitude passing through the original site of the Royal Observatory, Greenwich, England.
Progressive wave. A wave of moving energy in which the wave form moves in one direction along the surface of the medium.
[Q.sub.1]. Larger lunar elliptic diurnal constituent; with ([M.sub.1]), it modulates the amplitude and frequency of the declinational effects of the Moon and the Sun.
Refraction. The bending of the wave crest due to changing depths.
Resonance. Tidal motions on Earth are forced motions resulting in large scale oscillations analogous to a swinging bob of a pendulum. If the energy imparted exceeds the limits of true oscillation, a state of resonance is said to occur. If the dimensions of a gulf or sea allow for a period of free oscillation equal to that maintained in the ocean, resonance may occur.
[S.sub.2]. Principal solar semidiurnal constituent; it represents this rotation of the Earth with respect to the Sun.
Salt marsh. A low-lying flat area of vegetated marine soils that is periodically inundated by saltwater.
Saros. The 18.03 yr cycle in which Moon, Sun and Earth return to almost identical relative positions; a cycle in which solar and lunar eclipses repeat themselves under approximately the same conditions.
Seiche. A standing wave oscillation of an enclosed or partly enclosed body of water that continues to oscillate after the generating force ceases.
Semidiurnal. Twice daily tides; having a period/cycle of approximately one-half of a tidal day.
Set up (of the wind). Flow of wind such that the water is driven toward the shore line.
Sidereal day. The time of Earth's rotation with respect to the vernal equinox.
Sidereal month. Average period (27.322 mean solar days) of the revolution of Moon around Earth relative to a fixed star.
Sidereal time. Time usually defined as the hour angle of the vernal equinox.
Sidereal year. Average period of the revolution of Earth around the Sun with respect to a fixed star.
Slack water. For a perfect progressive tidal wave, this occurs midway between high and low water.
Solar day. The period of Earth's rotation with respect to the Sun.
Solstice. Times of the year when the Sun stands above 23.5[degrees]N or 23.5[degrees]S latitude (about 22 December and 22 June).
Spring tide. Tide occurring near new and full moon, when the range of the tide is greatest.
Standard time. With few exceptions, standard time is based upon some meridian which differs by a multiple of 15[degrees] from the Greenwich meridian.
Standing wave. Type of wave in which the water surface oscillates vertically without progression between fixed nodes.
Storm surge. The local change in the elevation of the ocean along the shore due to a storm. It is measured by subtracting the astronomic tidal elevation from the total elevation.
Storm tide (storm surge). A sudden abnormal rise (positive) or fall (negative) of sea level due to change in atmospheric conditions along a coast. The sum of the storm surge and astronomic tide.
Synodical month. The average period of the revolution of the Moon around Earth relative to the Sun's position (29.531 days).
Thalweg. The median line of a stream or channel.
Tidal bore. A tidal wave that propagates up a relatively shallow and sloping estuary or river channel with a steep wave front, the leading edge rises abruptly, often with continuous breaking and commonly followed by several large undulations.
Tidal constituent (partial tide). A cosine curve representing the influence or characteristic of the local tide.
Tidal creek. Is a creek formed by tidal water that moves onto a tidal marsh during the Higher High Waters, discharging with the turn of the tide.
Tidal curve. See "marigram".
Tidal day. The time interval between two successive passes of the Moon over a meridian (about 24 hours, 50 minutes).
Tidal estuary. The mouth of a tidal river where the tidal flow regime shapes the channel bed.
Tidal prism. The top part of the estuary between the Low Water and the High Water levels.
Tidal range. Total vertical distance between High Water and Low Water. Note. In Canadian Tide Tables, the range at a given location is the distance between Higher High Water and Lower Low Water.
Tidal river. The stretch of a fresh water river where the dominant factor shaping the channel is fresh water.
Tide. The periodic rise and fall of a body of water resulting from gravitational interaction between Sun, Moon and Earth.
Tide producing force. That part of the gravitational attraction of the Moon and Sun which is effective in producing the tides on Earth.
Tide wave (tidal wave). Long period gravity wave originating in the tide-producing force and manifest in tidal ebb and flow.
Tiding (warping). Transformation of salt marsh into grasslands by use of canals to focus tidal inundations of sediment-charged seawater.
Tractive force. The horizontal component of a tide-producing force vector.
Tropical monthly cycle. The average period (about 27.322 days) of the evolution of the Moon around Earth relative to the vernal equinox.
Trough. The lowest point in a propagating wave.
Tsunami. A seismic sea wave; in literal translation from Japanese meaning "a long wave in harbour".
Universal time. Same as Greenwich Mean Time.
Vernal equinox. See "equinox".
Wave height. The vertical distance between crest and trough.
Wave length. Horizontal distance between two successive wave crests or troughs.
Wave train. A series of waves from the same direction; also known as a wave set.
[Z.sub.0]. Symbol recommended by the International Hydrographic Organization to represent the elevation of mean sea level above chart datum.
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 5: Chapter 11-Appendix|
|Author:||Desplanque, Con; Mossman, David J.|
|Date:||Mar 1, 2004|
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