Stuff about Tides

As a young lad growing up in Minnesota, I was aware that the ocean had tides but really knew nothing about them. In 2006 or so I began sea kayaking in the Georgia Strait and then elsewhere on the ocean. So, I learned about tides. This article tries to explain a few things about tides. At the end of this piece, I explain the Rule of Twelfths, a very useful rule for the sea kayaker. The Internet can be a useful tool in learning about tides, but beware - there is a lot of incorrect information out there. In particular, there are some web sites and even textbooks, that explain tides as due, in part, to centrifugal force. Centrifugal force is a fictitious force, quite useful in reference frames that are rotating with respect to an Inertial Frame. However, tides are due to gravitational effects, not to the fictitious centrifugal force. Tide tables are available on the Internet for many locations. These are extremely useful. Sometimes you also need local knowledge as a supplement or maybe that’s all that is available. What follows attempts to explain tides without appealing to mathematics, in an effort to be useful to the widest audience. A more thorough discussion appears in this book (which is also relatively non mathematical): Chapter 7 of Bad Astronomy by Philip Plait, Wiley (2002). Ultimately, any deeply interested person needs to go to a mathematical explanation, outside the scope of this discussion. Further, many of the numbers we use here will be approximate. The Tidal Bulges The moon is the major contributor to ocean tides. The sun is also a contributor, exerting about half the contribution made by the moon. For starters, we will talk about the gravitational effects of the moon and then about the sun. The gravitational attraction between two masses decreases the further apart the two masses are. So the point on Earth closest to the moon feels the greatest gravitational attraction to the moon. This will deform the Earth very slightly and, as a fluid, water shows this effect most strongly and the ocean will bulge slightly toward the moon. The point of Earth furthest from the moon will feel the least gravitational attraction to the moon, so that point opposite the moon will also experience a bulge, being attracted less strongly to the moon compared to its surroundings on earth’s surface. So there are two tidal bulges on Earth, one closest to the moon and one furthest from the moon. The moon orbits the moon in about 28 days, meanwhile the Earth rotates once each day. Hence the earth rotates through the two bulges each day. So there are typically two high tides and two low tides per day, and we term such tides as semi diurnal. The high tide to low tide change takes about 6 hours and 12.5 minutes; and from low tide to the next high tide, another 6 hours and 12.5 minutes. These are idealized numbers and in the more complicated reality, these numbers can vary significantly. Nevertheless, in somewhat typical tidal areas, these numbers remain useful for gross estimates. Note that the vertical distance from one high tide to the adjacent low tide is called the tidal range. From the above, note that the first high tide tomorrow occurs 50 minutes later than the first high tide today (24 hours and 50 minutes later). Moonrise occurs 50 minutes later the next day than today. This should not be a surprise, since the moon drags the two tidal bulges along ‘underneath’. What about the effect of the sun? Its effect on tides is about half that of the moon, so its effect is not trivial. This is easiest to see with the tidal bulges. When the sun, earth, and moon lie in a straight line (full moon and new moon), the effect of the sun adds to that of the moon. In that case, the bulges get bigger i.e. bigger high tides. These are called spring tides. When sun, earth, and moon form right a angle (the two quarter moons), the bulges get smaller i.e. smaller high tides. These are called neap tides. Mid Ocean Tides and the Effects of Land Masses Mid ocean tidal ranges are not large, less than a few feet. However, it gets more interesting when the tide runs into land masses. The tide is forced into channels around islands with complex shorelines, up rivers, and so on. Even the sea floor, if not too deep, has an effect. It becomes quite complicated. High and low tides then can exhibit potentially large ranges. Perhaps the most extreme tidal range occurs in Nova Scotia’s Bay of Fundy, which at its largest is about 56 feet. The largest tidal ranges I’ve experienced in the Georgia Strait are about 14 feet. One high tide may be the same height as its adjacent high tides, same for low tides compared to its adjacent low tides. As mentioned earlier, these are the semi diurnal tides. However, one high tide may differ noticeably from its adjacent high tides, same for low tides compared to adjacent low tides. These are called mixed semi diurnal tides. Further, there are places where the tides are diurnal (once per day). On the west coast of North America we typically see mixed semi diurnal tides. For an example, looking at the tides near Surge Narrows off Quadra Island we see on Wednesday September 11: • 3:56 AM PDT 11.84’ High Tide • 10:50 AM PDT 3.41’ Low Tide • 6:03 PM PDT 13.98’ High Tide • 11:47 PM PDT 8.40’ Low Tide which are mixed semi diurnal, typical in that region. Notice the time differences, not the idealized numbers but somewhat close. Also note the tidal ranges. In contrast, we can look at the Gorge in Victoria BC, where the tides are diurnal e.g. on Nov. 28, 2018 we see: • 3:56 AM PT 5.2’ Low Tide • 2:42 PM PT 8.4’ High Tide and the next day • 4:25 AM PT 5.2’ Low Tide So you do need to look at the tide tables! Further Complications What we’ve discussed so far is, to a great extent, good enough, but there are other significant effects. The moon’s orbit around earth is elliptical not circular. When the moon is in perigee (closest to earth) its gravitational effect is stronger than when it is in apogee (furthest from earth). Further, the plane of moon’s orbit is tilted with respect to earth’s equator, which is referred to as the moon’s declination. The moon will be a bit north sometimes and a bit south at others, again affecting the gravitational attraction from the moon. The elliptical orbit of the moon and its declination affect the size of the tide. So on North America’s west coast if the moon is in perigee, north, and aligned with the sun in its effect on the earth, then we can expect large high tides. These three events rarely coincide, but can. Similar effects occur due to the fact that earth’s orbit around the sun is also elliptical. Earth is closest to the sun (perihelion), around January 2, and tidal ranges are enhanced. Earth is furthest from the sun (aphelion) around July 2, and tidal ranges are reduced. There is also a delay of one to three days from the time of an astronomical event and its effect on the tides. So, for example, a large high tide will occur about one to three days after the full moon. Finally, extreme weather events can obviously modify the tides, making the tide tables much less accurate. In most case where there is extreme weather, we flatwater kayakers stay on shore and read a book. So watching the weather forecast and tapping into local knowledge becomes important. Rule of Twelfths Most places I have paddled on the sea have ‘mixed semi diurnal tides’ (the Victoria BC Gorge being the exception). Recall that this means that there are typically two high tides and two low tides per day (semi diurnal) and that the two high tides are of different heights and that the two low tides are of different heights (mixed). Recall that from low tide to high tide takes 6 hours 12.5 minutes ... and from high back to low, another 6 hours 12.5 minutes, the idealized numbers. The sea level change from high to low tide (or vice versa) is not linear, looking more like a sinusoidal shape. For example, if we start to evolve from low tide to high, the sea level increases slowly then accelerates then slows back down until high tide is reached. The 'Rule of Twelfths' gives a quick estimate of the expected tidal level at various times during the level change. Rule of Twelfths • In the first hour the tide level changes by 1/12 of the range. - slow • In the second hour the tide level changes by 2/12 of the range. - moderate • In the third hour the tide level changes by 3/12 of the range. - fastest • In the fourth hour the tide level changes by 3/12 of the range. - still fastest • In the fifth hour the tide level changes by 2/12 of the range. - back to moderate • In the sixth hour the tide level changes by 1/12 of the range. = back to slow Note that the above assumes 6 hours; adjust for the actual time interval. On the average, it is very close to 6 hours 12.5 minutes - but you should still adjust for the actual time interval. So if the time interval is not 6 hours then the one hour becomes total time interval divided by 6. A Practical Application Let’s say that on Thursday, Sept. 12, 2019 we decide to paddle from Discovery Islands Lodge to the Octopus Islands. We would choose to go through Surge Narrows at slack as we head NW. This occurs at ~10:05 AM. Once through we typically take a break at Yeatman bay (say 10:31 AM) and some like to take the hike into Main Lake. So what is the tide going to do to our kayaks while we’re gone? Looking at the tides I see for Thursday: • 04:49 AM PDT 11.97 ft High Tide • 11:31 AM PDT 03.51 ft Low Tide • 06:31 PM PDT 14.04 ft High Tide with the next low tide being at 12:22 AM, early the next morning. So between our landing at 10:31 and low tide at 11:31, the sea level will drop by 1/12 of the range (11.97-3.51) ft/12 = 8.46 ft/12 = 8.46 inches (not quite right yet) Fussing Further doesn’t matter much here. Nevertheless our result is not quite right, because the time difference from high to low is 6 hrs. 42 min. not 6 hrs, exactly. So the step change is not 1 hour, but 1 hour 7 min. Hence between a somewhat earlier landing at 10:24 and low tide at 11:31, the sea level will drop by 1/12 of the range i.e. by the 8.46 inches. This is all approximate anyway, so being off by 7 minutes hardly matters. Remember too that the tide table itself is not precisely for Yeatman Bay. The point is that if we’re back within 45 minutes our kayaks will be higher and drier than when we left them. But if we delay too long, the tide will rise again. And what if we are significantly delayed on our walk? I always suggest that we tie up the kayaks anyway and even leave someone behind to mind the boats. Note: the tidal range here from low then back to high is decent, over 10 feet. Recall that there are places where ranges over ~6 hours can be 56 feet (e.g. Bay of Fundy) so these calculations become more crucial.