on the subject of inter-tidal Progressions

In a letter from Dave Reynell, he tells of his 12 foot wooden dory which he rows on the Knysna estuary. The best rowing times he explains are during the neap phases since the tidal range is small resulting in gentler currents. He has observed that the inter-tidal progression between high tides during the neap phases vary from those during the spring phases and enquired as to the reason for this.

I would like to illustrate that this phenomena can be observed via pure geometric superposition (addition) of two curves which stand in an approximate ratio of 2:1 to each other and continually vary in phase.

To get everybody on the same page first, let me define inter-tidal progression as understood in this article and also demonstrate this phenomena by showing some examples from predicted data. If - for example - the spring high tide in Durban is at 3pm today and tomorrow the corresponding high tide is at 3-30pm then the inter-tidal progression is 30 minutes. In other words, it is the time difference of corresponding tides on successive days. During the neap phases the inter-tidal progression of the high tide is often 80 minutes - a significant difference!

The following illustrations use data from Durban since it will negate the possibility of an exclusive estuary effect. The images show a tidal progression from spring via neap to spring. That is a period of approximately 14 days - or the time taken by the moon to progress from a new moon to a full moon or visa versa

No.1 depicts a rather weak spring tide in comparison with the much stronger tide in No2.

The orange dots show all the predicted tides for the specific year.

By visual inspection it is very clear that the inter-tidal progression varies during the spring and neap phases. The tide advances during the neap phase. In addition we see an increased advance - important as we shall see later - when the tidal range is greater as in No2.

A further demonstration of the mentioned variations can be seen in the following barcode-style depiction of inter-tidal progressions taken over a period of 3 months.

The above should serve to confirm Dave Reynell's observations. Now to an explanation. I am no hydrographic expert, however, I would like to propose that the reason can be illustrated by means of simple geometry as follows:

Lets take two sine-wave curves which have the same frequency and stand in ratio 2:1 with regards their strength (amplitude). We draw them on-top of each other to start off with. The smaller (yellow) curve remains fixed whilst the larger blue curve starts sliding along to the right through an entire cycle of 360deg. As the blue curve slides along we mathematically add the yellow and blue curve together. The result is shown in the white curve. Finally we map all the white curves over each other.

The overlay of the white (resultant) curves clearly shows the different progression rates of the curve extremeties. Slower at the peaks and faster through the troughs. This effect can thus be achieved by simple geometric superposition of two pure sinus curves. The image below accentuates this result.

The final aspect to demonstrate is the effect of the ratios between the two signals on the respective advance. As can be seen, the signal ratio is of utmost importance. The larger the difference between the two signals (4:1), the less the effect in question. The closer the signals are in strength (4:3) the more the effect is accentuated.

In conclusion. There are very many factors which influence tidal behaviour. The main drivers however are the moon and the sun. It appears that the variation in the inter-tidal progression during the neap and spring phases can be understood by virtue of regular geometry - provided there are two dominant contributing factors which stand in a ratio of 2:1 to each other. Fortunately this is approximately true for the contributions made by the moon and the sun on our tides. All we need to do is associate the blue curve with the moon and the yellow curve with the sun.

Anton Feun
Ocean Rhythm