Actually, Faldage, my book lists something like 12 different components of tidal periods. (There are irregularities in planetary orbits and also the effects of the other planets which are small but affect things in the long run.) And I understand that the way they do tide charts these days isn't from modelling, but from harmonic analysis. Rather than trying to explain why the components observed dominate in one particular place, they just observe it and extend the observations into predictions.
Back to the Fraser River example...my supervisor says someone tried to model that particular location but he doesn't think they got as far inland as we were...sometimes there's a lack of data...so I guess to some extent there's not much use in modelling when you can just use harmonic analysis and build the tide table quite easily. The guys who drive the tugboats probably don't care about the why of the tide so much as the when and where of it!
I had some nifty plots of not-very-sinusoidal looking tidal patterns in my book but I'm at home sick again (I made it into school this morning and gave up after a couple of hours) and can't scan them for you.
Edit: I've given it some thought and I do agree with Faldage: the tide you observe from day-to-day seems sinusoidal - but the overall picture, observed over many days, or a month, is not just a plain old sine curve, or even a superposition of just two frequency components, but much more complicated than that.
