Tides

Editor's Notes

• #33: http://home.hiwaay.net/~krcool/Astro/moon/moontides/TideAni.gif
• #67: The tide The tide, the motion of ebb and flood in the sea. This is a phenomenon seen by everyone who has ever been to the seashore. Water rises and subsides again just as regularly. For most of us, this rhythm is a fact, a natural occurrence that was always there and always will be. There is a reasonably simple explanation for it, though. As early as the third century BC, Aristotle linked tidal motions to the moon. In 42 AD, Pliny the Elder gave a fairly exact description of the phenomenon and its connection to the sun and the moon. The oldest extant tide tables were compiled by an English monk in the 13th century; but doubtless, some sort of tidal predictions must have existed already in prehistoric times.   The word getij in Dutch, the English word tide and the German word Gezeiten all derive from the word time. That itself shows that the tide is inextricably bound up with time, which is logical if we consider that tidal motions are based on the apparent motions of the moon and the sun about the earth. Because the motions of these two celestial bodies are very constant, the rhythm of ebb and flood is too. On the following pages a description is given of how tides begin at sea and what happens on the Dutch coast. This explanation is for the greater part the same as the equivalent chapter in "Het getij & wij". This book (in Dutch) was published by Sdu publishers in the Hague on the occasion of the celebration of the hundredth edition of the "Dutch Tide Tables". The authors are Eric Burgers and Ruud Hisgen of Direct Dutch in the Hague, together with contributors from the National Institute for Coastal and Marine Management /RIKZ . Meanwhile this book is out of print.   This account is about ten pages long. You can read right through, which we recommend, or separately, in whatever order you please. © 1998, National Institute for Coastal and Marine Management / RIKZ Last update:
• #68: The Equilibrium Tide As early as the 17th century, Newton explained how the tide works. Let us follow him and imagine the earth without continents, covered in water of the same depth everywhere, and only the gravitational force of the moon. The tide occurring in such a situation is called the equilibrium tide. There is a mutual gravitational force between the earth and the moon. This force causes moon and earth to orbit each other in an eclipsic path. Because the earth is much more massive, the common centre of gravity is about 1700 km below the earth’s surface. Relative to this path the attractive force of the moon and the centrifugal force cancel each other out, as far as the earth as a whole is concerned. But, as the diagram shows, this is not the case for specific points on the surface of the earth. On the side of the moon the attractive force exceeds the centrifugal force, on the opposite side it is just the other way round. Due to this, the earth is moulded like a rugby ball, with the two sharp sides facing and averted from the moon. The film of water, which the ocean constitutes, is deformed much more than the solid earth. Due to the rotation of the earth around its own axis, the deformation of this film revolves in the course of a day. In this way, an observer from an island in this hypothetical world-wide ocean would notice each day twice a high water and twice a low water. Newton supposed that the deformation could propagate in such a way that there would be a constant equilibrium of forces everywhere. His theory is, therefore, known as equilibrium theory.
• #69: Times of Tide In the previous section we have seen why ebb and flood occur twice a day. But as every true-born marine expert knows, the time between one high tide and the other is not 12 hours, but 12 hours and 25 minutes, i.e. a difference of 50 minutes each day. How can that happen? To find the answer to that we have to take a look at the way in which the moon orbits the earth. The moon orbits the earth along to an elliptic path. After 27.32 days, the moon has completed one orbit. That orbit is called a tropical lunar month. The moon orbits the earth in the same direction as the direction in which the earth revolves around its axis. After one day, the moon has shifted slightly in its path. A particular point on earth (for instance where there is high tide) is not in the same position relative to the moon as it was 24 hours ago. The earth will have to revolve a bit further to ensure that that point on earth is in the same place relative to the moon. It takes the earth well over 50 minutes to do that.   You can calculate this as well. As seen from a distant point in the universe, the earth rotates around its axis in 23 hours and 56 minutes ( see the following section ) That is approximately 15 degrees per hour (360 degrees divided by 23 hours and 56 minutes). It takes the moon 27.32 days to orbit the earth once. Therefore the moon shifts approximately 13 degrees per day (360 divided by 27.32). The earth then needs 13/15 hours, which equals about 50 minutes, to catch up with the moon again. Based on a 24-hour day, the moment of high tide shifts an average of 50 minutes each day. With high tide twice a day, it returns on average after 12 hours and 25 minutes.
• #70: The earth-sun system The moon provides the largest tide-generating force on earth. But the sun, which is 27,000,000 times heavier than the moon, also has a gravitational pull on the earth. Given that the strength of the gravitational pull also depends on the distance between the celestial bodies and that the sun is 389 times further from the earth than the moon, the pull of the sun is only 45% that of the moon. (The reason for this is that the tidal forces are proportional to the mass and inversely proportional to the third power of the distance, therefore: 27,000,000 : 389 3 = 27,000,000 : 58863869 which is approximately 0.45).   It takes the earth one year to revolve around the sun. After 365.25 days the earth has completed one orbit. This orbit is called a tropical year. The orbital direction of the earth around the sun is the same as the direction in which the earth revolves around its own axis. It takes the earth 23 hours and 56 minutes to revolve around its own axis. After this orbit, the earth is not yet in the same position with regard to the sun. Each day the earth revolves about 1 degree further in its path around the sun (360 degrees divided by 365.25 days). As was explained in the previous screen , the earth revolves about 15 degrees per hour around its own axis. So it still has to go on revolving for 1/15 hour, i.e. 4 minutes, to reach the same position with regard to the sun. It thus takes the earth 23 hours and 56 minutes plus 4 additional minutes, i.e. exactly 24 hours, to return to its original position. This is the day we all know, the average solar day. Consequently, the tide generated by the sun yields a high and a low tide precisely twice each day.   But let us go back to the moon for a moment. In the time it takes the moon to pass once through its path around the earth, the earth-moon system has completed part of its path around the sun. That way it takes slightly longer than the 27.32 days mentioned earlier, that is to say 29.53 days, before we can see the moon at the same angle vis-à-vis the sun. This cycle is also called the lunar month or the synodic lunar month. © 1998, National Institute for Coastal and Marine Management /  RIKZ Last update:
• #71: Spring tide and neap tide When the sun and the moon are aligned with the earth as it were, they join forces and attract more water. We call this spring tide. In that case, the water level at high tide is higher and at low tide lower. The moon and the sun can also counteract each other. That occurs when the two celestial bodies are at right angles to one another. Then water is attracted from two different sides and as a consequence the water rises far less than average. This phenomenon is called neap tide.   Spring tide occurs twice per lunar month (every 29.53 days). You would expect there to be a spring tide at full moon and at new moon. However, this occurs two days later. Why this is, is explained in a later screen . The orbit of the moon is generally at a certain angle to that of the path of the earth around the sun. Consequently, sun, earth and moon are rarely ever aligned. But when they are, then there is a lunar or a solar eclipse.  The solar tide, with a cycle of 12 hours, continually catches up with the lunar tide, which has a cycle of 12 hours and 25 minutes. The effect is that the lunar tide is subjected to fluctuation: it is cyclically reinforced and weakened. It also has an effect on the timing of the tide. Between spring tide and neap tide, the solar tide has a priming effect on the tide, between neap tide and spring tide a retardatory effect.  
• #72: Diurnal inequality The average angle of the earth's rotational axis in relation to the connecting line between earth and moon is 66.5 degrees. The same applies in relation to the sun. The angle of the terrestrial equator is 23.5 degrees (90-66.5) in relation to the connecting line between earth and moon (and thus earth and sun as well). The ellipsoid of the water mass will be oriented towards the moon. During a complete orbit (one day), someone at a particular spot on the earth will therefore observe two high and two low tides which are unequal in height. This is called diurnal inequality.   At certain spring tides, the diurnal inequality is substantial. The subsequent inequality will, on the contrary, be insubstantial. This has to do with the point, or the node, where the lunar path intersects the ecliptic surface. The ecliptic surface is the surface formed by the orbit of the earth and the sun. The sun, earth and moon are then as far as is possible in one plane. The cycle between two nodes is 27.21 days. This gradually catches up with the lunar month cycle of approximately 29.53 days. After about 13 lunar months, that is about 376 days, they are level again. Therefore, the inequalities are not systematically larger during either new moon or full moon. In addition to the diurnal inequalities, there are other variations in high and low tide levels.
• #73: Variations Spring tide occurs twice a month, after a new moon and after a full moon. In general, two successive spring tides differ in strength. The main reason for this is the elliptical lunar path. If, during any one spring tide, the moon is close by, then it will as a matter of course be far away at the next spring tide. In the first case, the spring tide is higher than in the second case. As stated before, the moon takes about 27.32 days to complete its elliptical path around the earth. So it gradually catches up with the cycle of the lunar month, which is about 29.53 days. After some 15 lunar months, i.e. about 440 days, they coincide again. Therefore, spring tides are not systematically stronger during either new moon or full moon. We can see a variation in spring tide height, the highest spring tide at times being at new moon and at other times at full moon. Both cycles last approximately six months and are produced by the previously described cycle of 440 days and the cycle of 376 days described above. Both cycles are nearly equal to a calendar year.   There are all sorts of other cycles brought about by the separate revolutions of the earth and the moon around one another and as a system around the sun. The most important of these are: the 8.85-year cycle which is the result of the fact that the long axis of the ellipse of the moon's path rotates around the earth during this length of time, and the 18.6-year cycle. In this period, the angle at which the moon is in relation to the equator plane of the earth fluctuates between 18.5 degrees and 28.5 degrees. The 23.5 degrees mentioned in the previous screen is an average.
• #74: The astronomical tide Until now we have assumed, together with Newton, that the whole world was covered with water. Our starting point was the so-called equilibrium tide. The real situation is of course more complicated, because as there obviously are land masses on earth and it is not equally covered with water. Continents and islands are obstacles along the way, and the seas are not the same depth everywhere. The only exception is a strip of water in the vicinity of the Antarctic Ocean, at 55 to 65 degrees southern latitude, which is not interrupted by land and where the tidal wave can propagate freely. The locations of the obstacles are, of course, quite stable. On the basis of this situation we may expect a large measure of regularity, including all cycles shown in previous screens. This predictable (and thus calculable) tide is called the astronomical tide. This is also the tide we can find in tide tables. This information can be predicted fairly accurately over a period of years in advance. Changes in the shape of the coastline, for instance the building of dams or the like, can have a disruptive effect.   So our tidal motion has its origin in the southern hemisphere. The tidal wave that is generated here flows northwards through the Atlantic Ocean. On its journey, it is variously deformed by the structure of the ocean. After two running days, the tidal wave reaches the Arctic Ocean. In the course of this journey, it undergoes a deflection that is the result of the earth's rotation. This Coriolis Force faces to the right in the northern hemisphere. Apart from that, the Atlantic Ocean is so large that the tidal cycle is about equal to the ocean's own cycle. This way a latitudinal stationary wave arises, as a consequence of which the heights of the tides at the edge of the ocean are higher than would be expected by reason of gravitational pull alone.   In reality, in the field so to speak, there are more factors that influence the water height. Atmospheric pressure plays a minor part, while wind force as well as wind direction are of more importance.
• #75: Age of the tide When the tidal wave reaches the North Sea, it has a long journey behind it. It has then already crossed the greater part of the Atlantic Ocean. The time between the origin of the high tide in the Antarctic and its arrival is called the age of the tide. So, depending on where you are, the tide can be young, mature or advanced in age. Off Brest, for example, the tidal wave is about 29 hours old. On the other hand, it takes the tide 52 hours to reach IJmuiden. The reason for this is that it follows a longer route around the British Isles. The tide off the entire Dutch coast is already at least two days old.   When the tidal wave is near the British Isles, it enters the North Sea from two different directions. First of all, the wave moves further to the west along the Irish coast and the British coast in a northerly direction and then goes around Scotland. Because the opening is at its largest there, this branch of the tidal wave has the greatest effect in the North Sea. The Coriolis Force compels the current to make a kind of anticlockwise circular motion through the North Sea. The tidal wave then propagates itself along the British coast towards the south and then turns again along the Belgian and Dutch coast in a northerly direction towards Denmark and Norway. Another part of the Atlantic tidal wave approaches the Channel from the south at an average speed of 200 metres per second and is then, to a large extent, blocked. A damming up of the water then takes place, which results in a considerable tidal difference off the coasts of southern England and Normandy. When the current has then squeezed through the Channel, it has by that time lost most of its velocity and force and for that reason it has only a minor influence on the coast of the Netherlands.   By making several observations (and assimilating them in mathematical models), lines can been drawn on the North Sea where simultaneous high tides occur. These so-called cotidal lines may be drawn for simultaneous low water, or for equal phases of the separate harmonic constituents , as well. The lines of simultaneous high water in the figure show that there are two points in the North Sea where the lines intersect and around which the tide rotates. At these nodes there is almost no tidal motion at all. They are called amphidromic points.
• #76: Tidal ranges along the coast Because of sea bed configurations, coastal shapes and all sorts of other side effects, the North Sea has a complicated system of tides. Tidal curves from several measuring points along the Dutch coast indicate mutual differences between high and low tide levels. The largest tidal ranges in the Netherlands, approximately 4.80 metres between high and low tide, occur near Bath at the back of the Westerschelde, because of the damming up of the tidal wave in the estuary. From Flushing there is a marked decrease in the tidal range along the coast in a northerly direction. At Den Helder the effect is a minor one because of the proximity of the amphidromic point ( see previous page ), after which it increases again gradually. The difference in duration of ebb and flow can be calculated from the tidal curves. In Harlingen it takes about 4 hours and 58 minutes before the water is at its highest, but 7 hours and 27 minutes before it is low tide again. So ebb lasts far longer than flood. The same phenomenon can also be observed in other places. The explanation is to be found mainly under water. The tidal wave moves forward at a specific velocity. The deeper the sea, the more freedom of motion there is. During the length of time of ebb and flow, the ocean tide hardly displays any asymmetry. The North Sea, and especially the Waddenzee area, are not so deep, however. If the flow is pushed through between the islands towards Harlingen, then that takes place at full force. The water undergoes considerable resistance from the very shallow Waddenzee sea. When the water has to return at low tide after the flow, then the damming force of the North Sea is no longer there, but the resistance of the sea bed obviously still is. That is why ebb takes much longer to dispose of the water than flow needs to bring it in.   Along the Dutch coast and inland on the rivers, a strange phenomenon can be observed. As can be seen from the tidal curve of Hook of Holland (at the beginning, on the left), once the water has reached the lowest level, it remains so for some time. After rising slightly, it then drops again and a second low tide follows. Only then does the water rise quickly and the flood sets in. A slight rise like this followed by a drop is called an agger or a double tide. In Den Helder, the same kind of phenomenon occurs, but this time during high water. The high water is stretched, as it were. Here the term used is not agger but a double high water. The strength of this phenomenon is dependent on time and place. The proximity of the amphidromic point at about 70 km off the coast point explains why at spring tide there is a larger agger and at neap tide a smaller one ( see previous page ), This point weakens the lunar tide, as a result of which other tide components come into play. Given that the cotidal lines of other tide components are very different to those of the lunar tide, these can cause aggers and the like to occur in certain situations. More information on this subject can be found in the last part.
• #77: The theory behind the culmination method is directly linked to Newton's theories. The word 'to culminate' means to reach the highest point. Using celestial values, the method is used to relate the time and the level of high and low tide to celestial variables, in particular the moment that the moon is at its highest, the so-called moon's transit. This method is especially useful in areas with a semi diurnal tide. Other celestial variables used for the methods are the lunar declination (the angle of the moon in relation to the terrestrial equator), the lunar parallax (a measure for the distance of the moon to the earth) and the season. In the Netherlands the Tide Tables up to 1985 were computed using this method. Until 1965, these computations were carried out wholly manually. The method was originally applied at five standard ports, after which the secondary ports were linked to this. As soon as the Deltaplan works came into operation, several problems arose. The large hydrological changes brought about by these works meant that each port had to have its own analysis made. The limitations of the method also became manifest, namely that only high and low tides (times and levels) can be calculated. However, intermediate values can be calculated using the other method and in 1986 this was introduced as a standard for all ports.
• #78: The harmonic analysis William Thomson, later known as Baron Kelvin (1824-1907) and George Darwin (1845-1912), Charles Darwin's son, developed the method of harmonic analysis, elaborating on ideas presented by Johannes Kepler (1571-1630), Isaac Newton (1642-1727) and Pierre Simon de Laplace (1748-1827). Here the tide is shown as the sum of a number of sinusoids, the cycles of which are equivalent to those of the motions of the sun and the moon. A sinusoid is therefore a harmonic component, characterized by a wave length and an amplitude. As we have exact knowledge of the motions of the earth, the moon and the sun, we are able to give a precise definition of the most important components (i.e. the wave lengths) in advance. The amplitudes and phases are then deduced from the water-level measurements with the help of least squares regression. At present, water level measurements are taken every ten minutes at quite a few gauges and centrally recorded at the RIKZ. These series of measurements are used for deducing the components. On the basis of the deduced components, high and low tides are calculated and published in tide tables. The most important components are (obviously) the semidiurnal lunar tide M2 and the semidiurnal solar tide S2. Another important component is a 'overtone' of the M2, the M4. This is a component with a frequency of 6 hours and 12.5 minutes. Likewise there exist 6- and 8-diurnal constituents, too. Where the semidiurnal tide is not too strong, these ‘overtones’ may cause the phenomena of agger or double high water described in a previous screen. To calculate the tides along the Dutch coast a set of 94 components is used. In the middle of the sea the coast has less influence and a smaller number of components suffices.   The RIKZ publishes a PC program with the help of which the astronomical tide for most locations can be calculated using harmonic analysis. You can look up how to order this Tide Generator or how to download a test version on another page . There also exists a book, now out of print, entitled " Het getij en wij" , published by Sdu publishers in The Hague. This popular science publication describes how tides come about and outlines the history of the theory of tides and tidal predictions. It was written by Eric Burgers and Ruud Hisgen of "Direct Dutch" in conjunction with a number of contributors from the Rijksinstituut voor Kust en Zee / RIKZ / National Institute for Coastal and Marine Management. © 1998, National Institute for Coastal and Marine Management /  RIKZ Voor het laatst bijgewerkt op