Why is there a daily inequality for low tides?

Question

I understand why there is a daily inequality for high tides. What I do not understand is why the low tides are not equal. The data all seems to be somewhere along the lines of
but the theory seems to point to
That is, a greater daily inequality for high tide and none for low tide. I know that there are things to consider besides the moons influence, but the data pretty clearly rises above the noise in its consistency.

Answer 1

The water for high tides needs to come from somewhere; the mean sea level should stay approximately constant, as long as wind is neglected. That way tides are a kind of oscillations.

In the first of the two diagrams a low low tide is followed by a high high tide, and a high low tide is followed by a low high tide. That way the mean sea level, averaged over one low tide - high tide period remains constant:

In the second diagram you need to average over two low tide - high tide periods to get a constant mean:

The first diagram can be explained by the superposition of semi-diurnal tides, while the second diagram needs an additional diurnal constituent. Depending on the amplitude and phase shift of the diurnal constituent relative to the semi-diurnal constituent we can get different resulting oscillations.

More about tides and their constituents.

Answer 2

You need to be careful about which port or beach you take the data from. It is not the same to measure tides on the eastern side of a gulf than on the western side, due to Moon's motion, and also it is not the same to take data at the far end of a gulf than on its mouth.

I think this last thing is what happens to your data.