Moon #2 - Mixed Semidiurnal Tides

The Mixed Semi Diurnal Tide

The place on the earth closest to the moon experiences a tidal bulge, and the location on the diametrically opposite side also experiences a tidal bulge. In a subsequent blog article we will explain why there are two such diametrically opposed bulges, but here we will discuss the effects of those two bulges. If earth were a perfect sphere covered by just water and no land masses, then as the earth rotates any given location would experience two equal high tides and two equal low tides each lunar day. However, the large land masses on the planet complicate this significantly. The seas cannot move freely around the globe because they run into these land masses so that the tides establish much more complex patterns.

In those cases when the sun, moon, and earth fall on a straight line (full moon and new moon), the bulges will be larger, leading (within a few days) to higher high tides and lower low tides, hence larger tidal ranges. Recall from an earlier blog entry (Moon #1) we saw that from one moonrise to the next is about 50 minutes later the next day ... on the average. So the lunar day is 24 hours plus 50 minutes ... on the average. So those two high tides and two low tides fall within 24 hours plus 50 minutes ... on the average. Hence, from one high tide to the next low tide is 6 hours and 12.5 minutes ... on the average.

Typically, most areas have two high tides and two low tides each day. When the two highs and the two lows are about the same height, the pattern is called a semidiurnal tide. If the high and low tides differ in height, the pattern is called a mixed semidiurnal tide. There are even areas which have only one high and one low tide each day, which is called a diurnal tide. The areas where I paddle (the west coast from Washington through British Columbia) have the mixed semidiurnal tide (although the tides around Victoria, BC can be weirder). Here’s a representation taken from the Internet:

Notice that the horizontal axis is the lunar day i.e. slightly longer than the 24 hour day.

The situation with tides is complicated enough that extensive “tide tables” have been created to cover most areas of interest on the earth. It is very instructive to look at an extract and I’ll pick several days at Surge Narrows on the east side of Quadra Island in British Columbia, Canada.



2020-07-13 Monday

12:48 AM PDT 14.7 feet High Tide

1:08 AM PDT Moonrise

8:01 AM PDT 7.7 feet Low Tide

2:02 PM PDT 11.8 feet High Tide

6:09 PM PDT 8.7 feet Low Tide



2020-07-14 Tuesday

1:24 AM PDT 14.4 feet High Tide

1:26 AM PDT Moonrise

8:40 AM PDT 6.6 feet Low Tide

3:14 PM PDT 12.4 feet High Tide

6:59 PM PDT 9.8 feet Low Tide



2020-07-15 Wednesday

1:46 AM PDT Moonrise

1:59 AM PDT 14.1 feet High Tide

9:14 AM PDT 5.6 feet Low Tide

4:13 PM PDT 13.1 feet High Tide

7:52 PM PDT 10.7 feet Low Tide



Notice that we have two unequal high tides per day and two unequal low tides per day (mixed semidiurnal). Also, the lunar day is about 20 minutes longer than 24 hours, not at the 50 minute longer average. The maximum tidal range occurs on Wednesday from 14.1 feet (high) to 5.6 feet Low); so the range is 8.5 feet. And is the time from one high tide to the next low tide 6 hours and 12,5 minutes? No, it wanders around quite a bit. Now let’s move about a month later:

2020-08-10 Monday

5:20 AM PDT 7.4 feet Low Tide

12:12 PM PDT 12.0 feet High Tide

4:49 PM PDT 8.2 feet Low Tide

11:33 PM PDT 13.8 feet High Tide

11:49 PM PDT Moonrise



2020-08-11 Tuesday

6:11 AM PDT 6.7 feet Low Tide

1:32 PM PDT 12.2 feet High Tide

5:37 PM PDT 9.4 feet Low Tide



2020-08-12 Wednesday

12:00 AM PDT 13.5 feet High Tide

12:11 AM PDT Moonrise

7:04 AM PDT 5.9 feet Low Tide

2:43 PM PDT 12.7 feet High Tide

6:30 PM PDT 10.4 feet Low Tide



Monday and Wednesday are similar to the earlier table extract. But Tuesday looks more interesting. Did the moon not rise that day? Exactly so, but from the moonrise on Monday to the moonrise on Wednesday is 24 hours plus 22 minutes – so really no surprise. The lunar day is longer than 24 hours so if two successive moonrises are spaced just right they can occur just outside the boundaries of a day (Tuesday in our example). Further, Tuesday has two low tides, but just one high tide. That’s because the second high tide has just barely slopped over to Wednesday.

A Useful Application – The Rule of Twelfths

As mentioned earlier, most places I have paddled on the sea have ‘mixed semi diurnal tides’). 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. These are average numbers, with significant departures from those numbers as shown earlier.

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, close enough to the average value of 6 hours 12.5 minutes. You should now 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. Our rule of twelfths replaces ‘the hour’ by one sixth of the actual time between high and low tides.

A More Accurate Rule of Twelfths

• In the first segment (actual time/6) the tide level changes by 1/12 of the range. - slow

• In the second segment (actual time/6) the tide level changes by 2/12 of the range. - moderate

• In the third segment (actual time/6) the tide level changes by 3/12 of the range. - fastest

• In the fourth segment (actual time/6) the tide level changes by 3/12 of the range. - still fastest

• In the fifth segment (actual time/6) the tide level changes by 2/12 of the range. - back to moderate

• In the sixth segment (actual time/6) the tide level changes by 1/12 of the range. - back to slow

The Rule of Twelfths works particularly easily when tidal height values are expressed in feet. If the tidal range is 14 feet then the twelfth is 14 inches, or if the tidal range is 9 feet then the twelfth is 9 inches, and so on. Further, the sequence 1/12, 2/12, 3/12, 3/12. 2/12, 1/12 (versus time) agrees quite nicely with the actual sinusoidal shape of the tide level versus time.

A practical example:

We’ll create our own (realistic) data, but note that this sort of information (for many locations) can be downloaded from the Internet well before your trip. Let’s say we decide to paddle from Discovery Islands Lodge on Quadra Island, BC to the nearby Octopus Islands. As true flatwater paddlers, we would choose to go through Surge Narrows at slack as we head NW toward the Octopus Islands. From the current table (not shown), slack occurs at ~10:05 AM. It takes about 30 minutes to get through the narrows and on to Yeatman Bay. There we will take a break (maybe about 10:30 AM) and some of our group decide 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 tide table, I see for the day of interest:

• 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

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 (semi-accurate). 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 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 the hikers are back within 45 minutes, their 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 insist that we tie up the kayaks anyway and even leave someone behind to mind the boats.

Notes:

1. As seen, the tide falls for the hikers. After their return, the tidal range here from low then back to high is a respectable 10.53 feet. So if the hike starts late and/or is slower than planned, the tide will actually be rising again. There are places where ranges over ~6 hours can be 56 feet (e.g. Bay of Fundy) so these calculations become more crucial.

2. It took 6 hrs. 42 min. For the tide to fall from high to low, not that different from 6 hrs. In fact it can differ more significantly, so these calculations again become more crucial.