Is half tide height always the same? (All other things being equal)

[TLouth7]

To illustrate

If this can help to visualize it:
a) Imagine a place with only a perfect semidiurnal component (say 12 hours cycle to make it simple): starting from MSL, water will go up up up up during 6 hours, then down down down down for 6 hours until it crosses MSL downwards, then continue down down down for another 6 hours, before starting go up again. In this case, half tide will always be the same, MSL.
b) Imagine a place where there is only a monthly component, a 28 day cycle without any other component. Water will go up up up for 14 days, then down down down for the following 14 days, and so on. It will cross its "MSL" once every 14 days.
Now go in a place where you have the two, a) and b) combined: you will have the half tide of case a) which will move up up up for 14 days, then down for the following 14 days --> each half tide will not be the same, except once every 14 days.

You can visualise this with the online tool linked below. Set B (frequency of daily tide) to 6, set D (frequency of monthly tide) to 0.3. You will see that the combined tide (dotted black line) fluctuates up and down. You can play with the relative amplitudes.

Superposition of Sine Waves

I see this shape of curve on tidal curves on the East coast all the time.

 

[johnalison]

If by half tide you mean half way in height (not time) between successive high and low tides, then a quick check of tide tables shows there is a small variation, max 0.3 metres between springs and neaps in my area. Could of course be more taking into account meteorological conditions.

I tend to think that the simplest explanations are the best.

 

[Pye_End]

If by half tide you mean half way in height (not time) between successive high and low tides, then a quick check of tide tables shows there is a small variation, max 0.3 metres between springs and neaps in my area. Could of course be more taking into account meteorological conditions.

If by tide tables you mean predictive tide tables, you've got an excelent set if they take into account meteorological conditions!

 

[Mark-1]

I tend to think that the simplest explanations are the best.

In which case Lusty D nailed it with: "the middle of a sine curve is always in the middle regardless of amplitude.".

My question was a masterpiece of bad wording due to a total lack of appropriate vocab but after some reflection time I wanted to know:

1) If you strip out all the peripheral geographical/weather etc effects do tides follow a good approximation of a sine curve?

2) If so, does the middle of that curve have the same magnitude regardless of amplitude?

Turns out yes and yes to both.

Although, I appreciate now q2 is basically asking is the middle of something the middle, and you could argue in the long term that middle point varies with sea level. (At the moment upwards.)

Thanks everyone.

 

[Mark-1]

If by tide tables you mean predictive tide tables, you've got an excelent set if they take into account meteorological conditions!

These days when tide tables can be taken off mobile phones at the last minute factoring in pressure etc is entirely possible. Can't be long before someone does it.

 

[johnalison]

If by tide tables you mean predictive tide tables, you've got an excelent set if they take into account meteorological conditions!

Meteorological conditions were ruled out in the original question. ? The question also used the phrase tidal curve rather than sine curve. Since the predictive tables are based on past data as well as a formula, they present a reasonable set of figures to be working on, even if tidal records would be slightly more precise.

 

[lustyd]

To strip away a lot of the detail you can simply return to the rule of twelfths, which sailors have seemingly accepted as a truth for centuries. 3 hours after low water (aka "half tide") , 6/12 of the height is achieved. It's a rule of thumb but it's accurate enough for all practical applications.

While there are ways to be more accurate about prediction than this, they won't really contribute anything useful in the real world, so the half height at half tide is more than adequate. You could predict to within a millimetre the expected tide, but if a canoe passes you there will be enough wake to make that prediction moot!

 

[TLouth7]

1) If you strip out all the peripheral geographical/weather etc effects do tides follow a good approximation of a sine curve?

2) If so, does the middle of that curve have the same magnitude regardless of amplitude?

1. I would say that most tides follow a good approximation of a combination of sine curves. We are all familiar with the twice-daily curve, and the ~monthly curve that gives springs and neaps.

If you sum two or more sine curves of different frequency you can get a situation where the middle of the fast oscillation (mid-tide) moves up and down over the period of the longer oscillation. As I said above this effect is sometimes noticeable on the East coast.

 

[TernVI]

Given two sinusoidally curves with two amplitudes but the same frequency, the mid point will be the same.
If tides had no other influences then the answer would be Yes.

Where the tides have no other influences, they are very small and not very interesting!

 

[Pye_End]

Meteorological conditions were ruled out in the original question. ?

But my reply was to post 17 not the OP.

Post 17 noted observations in tide tables which did not support the theory that all half tides are the same, and suggested meteorological effects might explain the difference - which clearly is not the case if those tables are predictive.

 

[Alan S]

If by tide tables you mean predictive tide tables, you've got an excelent set if they take into account meteorological conditions!

Of course they don't take met conditions into account. What made you think that? or did I miss some humour?

 

[lustyd]

Of course they don't take met conditions into account. What made you think that? or did I miss some humour?

There's no reason at all that a modern solution couldn't take weather into account. We have weather predictions going out a month into the future, and we have tide data years ahead of time. Making a website which combines the two for more accurate prediction would be trivial.

As I said above though, there is not a lot of practical value in doing so (that I can think of, anyway) and so it seems nobody has bothered to create such a system.

Edit to add, actually that's probably not true. Racers might be very interested in an on the day tidal stream chart based on specific conditions. Some of them might even pay for the information. Before we get there though we'd need a considerably more fine grained tidal model of the location to create a predictive model.

 

[oldmanofthehills]

Davy S's site suggestion is good. In the Bristol Channel at Avonmouth by inspection, one high tide is about 1.7 metres higher above than the previous high but previous low is also 0.4m higher than its previous. Thus the mid tide as it makes the transition on that day is 0.6 metres out of general centre. In areas with normal 3 to 5 metre tide range the offset would be likely to be less and maybe 0.3m which is about the max others have suggested, and what I can see looking at Plymouth.

 

[lustyd]

I don't think that's right. The low may be lower or higher than the previous day, but 3 hours later it crosses the mid point which is the same height as the previous day - roughly the ordnance datum on that site. The incoming tide might then go higher, but just over three hours after that it crosses the same point. Due to the steepness of the sine curve at this point of transition the time won't fluctuate much for the mid point of height precicely because 3/12 of tide flows 3 hours after high or low water.

 

[johnalison]

Of course they don't take met conditions into account. What made you think that? or did I miss some humour?

I think we have got into a right muddle here. PE complains that my approval of your relying on tide tables for an approximation implies that my tide tables must take account of meteorological conditions, which was a complication that I was hoping to overlook as did the OP, and then complicates it by saying that he was replying to post #17 and not to me. I have no doubt that he understands all this but I'm not sure that I do.

 

[Roberto]

An example of non-semidiurnal components importance, which makes oscillate the half tide level of still "nice sinusoidal curves" ; two different periods in the same location, west coast of North America where most tides are mixed semidiurnal (two daily highs and low waters of different amplitudes), without going that far, Venice shows a similar pattern.
Semidiurnal components still exist but are relatively less important , the influence of longer period components becomes more visible. Horizontal line is MSL, average of half tide over a long long period.
One can notice half tide of one leg LW/HW - HW/LW is generally (very) different from half tide of adjacent cycles.
Also, on the graph above, the height of tide goes "more" below MSL, on the one below (at a few week interval) it remains more above MSL. By averaging a sufficiently long number of cycles of course it gives MSL.

 

[oldmanofthehills]

I don't think that's right. The low may be lower or higher than the previous day, but 3 hours later it crosses the mid point which is the same height as the previous day - roughly the ordnance datum on that site. The incoming tide might then go higher, but just over three hours after that it crosses the same point. Due to the steepness of the sine curve at this point of transition the time won't fluctuate much for the mid point of height precicely because 3/12 of tide flows 3 hours after high or low water.

One day there is a bigger tide and next day a lesser. As it transitions from the previous days high high to todays not so low it it does not have to move equal distances from the nominal mean, so the half tide height ( the height at the mid time interval) is a touch above the nominal mean . Alternatively one can regard it as the time when the water level reaches the nominal mean being offset from halfway between high and low tide times. Define 'Half-tide'

Its really only obvious on the more extreme tides and not that relevant to most practical sailing.

Roberto's contribution shows it nicely

 

[Skylark]

There was a on-line RYA Cruising Conference this past weekend and this included a 40 min video by Prof Ivan Haigh of Soton Uni. He developed tidal theory from very basic assumptions all of the way to Amphridromic Systems. Very good, fascinating and informative presentation, highly recommended if you are an RYA member.