Tide prediction at some locale is more of an empirical art rather than an analytic science. It essentially is a reduction of decades or centuries of historical tide levels at the locale to Fourier-like coefficients. Tides at a locale are modeled as a sum of various frequency components, each with a magnitude and a phase offset from some reference. The frequency components are based on the Earth's rotation about its axis, the orbit of the Moon about the Earth, and the orbit of the Earth-Moon system about the Sun. Given a sufficiently long historical record at some locale, mathematical techniques enable teasing the magnitudes and phases for each frequency component from the record for that locale.
There are issues with this approach that limit the usefulness of these tidal coefficients for future predictions. The utility of the computed coefficients to predict future tides declines as time passes. The coefficients occasionally need to be recomputed. One issue is that there's a lot of noise in the historical records; a decent storm will temporarily make the tides behave differently than the record would suggest. This noisiness alone means that the computed tidal coefficients are not perfect. This makes the accuracy of predicted tides decline over time.
Another issue is that neither the Earth's rotation rate nor the Moon's orbital rate is constant; the tidal models assume they are. Even without the noise, a set of tidal coefficients from a hundred years ago would be worthless today because of the small changes in those rates.
Yet another issue is that the oceans themselves change over time because of sedimentation, changes in mean sea level, and changes in the shapes of the oceans due to plate tectonics. An estuary filling with sediment will drastically change the high frequency overtones that result from interactions between the driving frequencies and the coast. The oceans' responses to each of the driving frequencies is a set of amphidromic systems. Each amphidromic system comprises a central point around which water waves rotate at the driving frequency. The nature of these amphidromic systems slowly change over time as the oceans change.