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Tide Formation—Tide Height

The content and activities in this topic will work towards building an understanding of how the earth, the sun, and the moon interact to influence the height of tides.

Tilted Orbit of the Moon

<p><strong>Fig. 6.10.</strong> The declination of the moon changes throughout the month, up to as much as 28.5˚.</p><br />

Although the gravitational force exerted by the moon is the strongest influence on the tides—followed by the gravitational force of the sun—other factors also influence tides. One of these factors is the angle of the moon’s orbit with respect to the earth-sun orbital plane. The moon’s orbital path around the earth is not in line with the equator. Instead, the moon’s orbit is tilted or angled from the equator (Fig. 6.10). As the moon completes its orbit around the earth, it is north of the equator for half of the lunar month and south of the equator for half of the lunar month. The moon is only directly above the earth’s equator for two days in the lunar month. The moon's angular distance north or south of the equator is called its declination. The moon’s declination changes throughout the month as the moon moves in its orbit around the earth.

 

The two tidal bulges track the changes in lunar declination. When the moon is north of the equator, the maximum lunar tidal bulge on the near side of the Earth is also north of the equator (Fig. 6.10 A). The locations of these bulges cause daily changes in the tide.

 

<p><strong>Fig. 6.11.</strong> (<strong>A</strong>) A “high” high tide would occur in Ensenada, Mexico at midnight when it is located near the center of the tidal bulge closest to the moon.</p><br />
<p><strong>Fig. 6.11.</strong>&nbsp;(<strong>B</strong>) Ensenada experiences a second high tide at noon. However, because Ensenada is no longer located beneath the maximum tidal bulge, it is a “lower” high tide than in A.</p><br />
<p><strong>Fig. 6.11.</strong> (<strong>C</strong>) Hypothetical 24-hour tide graph for Ensenada, Mexico.</p><br />


Imagine a person standing on a shoreline at midnight at 31˚ north (N) of the equator (e.g., Ensenada in Baja California, western Mexico, indicated by a green star in Fig. 6.11 A) when the moon reaches its maximum northerly declination of 28.5˚ N. Because the moon is nearly overhead in Ensenada, the observer is located where the tidal bulge is at its maximum and will experience a “higher” high tide of 2 m (Fig. 6.11 A). As the earth rotates, Ensenada will move away from the tidal bulge. Around 6 a.m., approximately 6 hours after high tide, the person in Ensenada will experience a low tide of 0 m. Around noon, approximately 12 and a half hours after the first high tide, the Mexican Pacific coast is as far away from the moon as it will get and will experience another high tide (Fig. 6.11 B). But this second high tide will be lower, only 1 m (see Fig. 6.11 C). This is because the tidal bulges are in line with the moon, and the moon is not directly above the Earth’s equator. At 12:30, the person in Ensenada is not located in near the tidal bulge maximum. Valparaíso, Chile, located 33˚ south (S) of the equator and marked with a red star in Fig. 6.11 A, is located directly the opposite the moon at noon and is thus experiencing its highest tide of the day at noon. Six hours later, around 6:40 p.m., the person in Ensenada experiences another low tide of 0.5 m.

 

 

Elliptical Orbit of the Moon

The moon does not orbit the earth in a perfect circle. The moon follows an elliptical orbit, coming closer to the earth and moving farther away (Fig. 6.12). At perigee, the moon is at its closest point to the earth—approximately 360,000 km away. At apogee, the moon is at its farthest point from Earth—approximately 410,000 km away.

 

<p><strong>Fig. 6.12.</strong> The elliptical orbit of the moon around the earth. At perigee the moon is closest to the earth, at apogee the moon is furthest from the earth. The distance between the earth and moon is not to scale and the moon’s orbit has been greatly exaggerated.</p><br />

The elliptical orbit of the moon has a major effect on Earth’s tides. At perigee, the moon's gravitational pull is strongest, and the lunar tidal range is largest; at apogee the moon’s gravitational pull is weakest, and the lunar tidal range is smallest.

 

The moon completes its elliptical orbit every 27.5 days. This period is different from the lunar month, which is 29.5 days (the time it takes for the moon to cycle from new moon, to full moon, and back to new moon). The reason for the time difference between the orbit cycle and the phase cycle, the lunar month, is that the earth and the moon are moving around the sun during these cycles. As the earth and the moon orbit the sun, the moon has to travel a greater distance to be in the same orientation relative to the earth and the sun, making the phase cycle last slightly longer than the orbit cycle.

 

Elliptical Orbit of Earth

Just as the moon follows a slightly elliptical orbit around the earth, the earth also follows a slightly elliptical orbit around the sun. On average, the earth is approximately 150 million km away from the sun. The earth is closest to the sun during the northern hemisphere winter months (approximately 147.5 million km away; Fig. 6.13). This point is called perihelion. During summer in the northern hemisphere, the earth is farthest away from the sun (aphelion, approximately 152.6 million km away). The earth completes one orbit around the sun every 365.25 days, a solar year.

 

<p><strong>Fig. 6.13.</strong> The elliptical orbit of the earth around the sun. The distance between the earth and the sun is not to scale and the earth’s orbit has been greatly exaggerated.</p><br />

The gravitational pull of the sun on the earth is greatest when the sun is closest every January, a position called perihelion. This is the time of the year when solar tides are greatest. During summer in the northern hemisphere and winter in the southern hemisphere, the earth is farthest away from the sun—aphelion—and the solar tides are smaller.

 

Weird Science: Seasons

 

Cyclical Changes

The declination of the moon, perigee, apogee, perihelion, and aphelion are all changes in the relative positions and distances of the moon and the sun in relation to the earth. All of these cycles affect the height. Although these cycles occur over different lengths of time, they are all predictable. It is rare that all of these cycles coincide to cause exceptionally high and low tides. Maximum tidal range is produced when

  • the moon is either new or full,
  • the moon is at perigee,
  • the earth is at perihelion, and
  • both the sun and the moon have the same declination, directly over the equator.

 

It has been calculated that this maximum tidal range occurs only once every 1600 years. The last time of this occurred was in A.D. 1700.

 

Practices of Science: Scaling

 

Tidal Geographic Factors

Factors that influence tidal range occur not only on a solar system scale, but also on local scales. Tidal ranges vary considerably at different points of a coastline due to seafloor features. When oceanic tidal bulges hit wide, shallow continental shelves the height of the tide is usually magnified. Conversely, mid-oceanic islands that rise steeply from the seafloor and do not have continental shelves have smaller tidal ranges. Mid-oceanic islands often have very small tidal ranges of 1 meter or less.

 

In narrow mouthed basins that are connected to the ocean, the tides often rise higher than in wide bays and harbors. This is analogous to pouring an entire can of soda into a short wide glass and a tall narrow glass. The soda will rise higher in the narrow glass, because there is not as much area to spread out as in the wide glass. The same amount of seawater will rise higher in a narrow basin than in a wide-mouthed harbor.

 

The moon’s gravitational pull affects water in every location on Earth, and its influence on the height of the tides is affected by the size of the basin of water. The Pacific ocean basin is large and holds a large volume of water. This means that the moon’s gravity has a large amount of water on which to pull. This is one of the contributing factors as to why the tides in the Pacific tend to be greater than the tides in other, smaller ocean basins and seas.  The underwater geography also has an effect on larger tides experienced in the Pacific ocean basin, as does resonance. The tidal range of an area on the coast of Alaska, which is in the Pacific ocean basin, is greater than the tidal range on the coast of Sweden, which is next to the Baltic Sea, an inlet of the Atlantic ocean basin, even though these areas are located at the same latitude. The underwater geography coupled with the larger volume of water in the Pacific ocean basin are the reason that the tidal range differs between these two places.  The Baltic Sea has much less surface area and is much shallower than the Pacific ocean basin. This is why tidal changes that can be observed in big lakes are minor compared to tidal ranges in the ocean and why tides cannot be observed at all in small lakes.

 

Activity

Activity: Modeling Amphidromic Points

Model tidal movement and height within ocean basins.

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Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.