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Tidal Prediction Part 3

Posted December 03, 2006 11:00 PM by Jorrie
Pathfinder Tags: Tidal prediction

Apart from the periodic astronomical effects, there are some non-periodic effects on coastal tides that are difficult to predict far in advance. One's first reaction tends to be that the topology of the coastline, harbor or estuary must play a non-periodic role.

Topology

The topology of harbors obviously plays a role in the arrival times of the highs and lows of the tides, but this is mainly catered for in the harmonic constituent parameters as a phase shift (i.e., a time delay). As shown in part 2, the amplitude of the tide as a function of time sums as follows:

A = m1Cos(2Πt/T1 - Φ1) + m2Cos(2Πt/T2 - Φ2) + ... + mnCos(2Πt/Tn - Φn)

The constants Φn determine the phase shift of each harmonic constituent. However, topology plays a role in conjunction with meteorological effects. Non-periodic variations in tidal heights are mainly caused by strong or prolonged winds and by unusually high or low barometric pressure.

Strong Wind

The effect of wind on sea level, and therefore on tidal heights and times, is very variable and depends on the topography of the area in question. A strong wind blowing straight onshore will pile up the water and cause high waters to be higher than predicted, while winds blowing off the land will have the reverse effect.

Storm Surges

Winds blowing along a coast tend to set up long waves, which slowly travel along the shore, raising sea level where the crest of the wave appears. These waves are known as storm surges. When the trough coincides with the tidal cycle for a location, it is called a negative storm surge.

Barometric Pressure

A difference of 1 millibar from the mean barometric pressure can cause a difference in height of 1 centimeter. A low barometer will tend to raise the sea level and a high barometer will tend to depress it. This is however a complex process that depends on the mean barometric pressure over a considerable area.

Changes due to barometric pressure seldom exceed 30 centimeters but, when the mean sea level is raised or lowered by strong winds or by storm surges, this change will be greatly enhanced.

Summarized from: Land Information New Zealand (LINZ)

The fundamental force behind the tides, i.e., tidal gravity, is fully discussed in the eBook Relativity 4 Engineers.

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Anonymous Poster
#1

Re: Tidal Prediction Part 3

12/05/2006 1:31 PM

Jorrie, very interesting, but I feel that the shape of the coastline and the depth of the waters must play a non-harmonic role in the tidal currents and heights. I mean, shallow water will retard the tidal wavefront significantly. So why is that not non-harmonic?

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#2
In reply to #1

Re: Tidal Prediction Part 3

12/06/2006 10:53 AM

Hi guest, you asked: "I mean, shallow water will retard the tidal wavefront significantly. So why is that not non-harmonic?"

As I (hopefully) pointed out in the original post, it is a bit of both...

A simple retardation of the wave front due to shallow water (or obstacles) will be harmonic - it's just a phase shift. However, the topology of the coast also works together with the coastal winds. This throws a non-harmonic component into the mix.

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#3
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Re: Tidal Prediction Part 3

01/05/2007 1:35 PM

Its easy to invoke winds, air pressure and surges but these just offer a smoke screen to clear thought. It doesn't shed light on the basic mechanisms such as the shallow water non-linear effects, these would still occur with no atmosphere or weather.

Lets draw an analogy. The tidal gravitational potential is like the input to an amplifier. The local transfer function is like the reponse of the amplifier. If the response is linear we just get the same frequencies out of the amplifier that we put in. OK some of them are phase shifted and some may have a different relative amplitude. But that is because of the frequency and phase response of the amplifier, not because of its non-linearity. This is the linear story which gives the linear harmonic components in tidal harmonic theory

Now consider the non-linear effects, the so called shallow water effects. Just like clipping in an amplifier, this generates higher harmonics of the original frequencies. Each with its own phase shift and amplitude. In the ocean - the tidal range can often be clipped at the its lower edge due to the existence of a shallow bar or ledge at the entrance to a harbour. At the maximum it can form a sharp peak from a wave building up.

Now to the question of the retardation of a wave front in shallow water. The very fact that the retardation applies to a wave which comprises those higher harmonics means that it is already a non-linear phenomena. Of course your really need to ask whether you are describing the retardation of the wave of an individual fourier wave component, or whether you are talking of retardation of the actual total physical wave (which is the sum of all of the linear and non-linear components).

As for the diurnal onshore / offshore wind - it may well add a very small drag effect, but it will have a frequency of once per day and will be subject to meteorlogical variation. The effects of seabed topology are far more important in most places and cause integer multiples of the M2 semi-diurnal component, which in any event is much larger in most locations.

That is the simple case. You are welcome to examine the manual to our tidal analysis suite for more information Geotide

Dr Steve Taylor

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#4
In reply to #3

Re: Tidal Prediction Part 3

01/05/2007 2:01 PM

Thanks, Steve, nice input. You wrote: "That is the simple case. You are welcome to examine the manual to our tidal analysis suite for more information Geotide"

The link does not seem to operate, or the page may just be temporarily unavailable. I would like to read more on it.

Regards, Jorrie

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#5
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Re: Tidal Prediction Part 3

01/05/2007 4:47 PM

Jorrie

Sorry the manual is at http://www.geomatix.net/tides/manuals.htm

The "simple case" is considering the components individually. In practice - to save time and calculation - there are tidal grouping of components.


Steve

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