It's possible to predict tide at a given location and at a given time reasonably well (e.g. predicting low tide). And there are tools available that make it possible to do this calculation for any location on earth at any time, such as OTPS.
Given that, it's possible calculate the annual maximum tide by calculating (sub)hourly data, and then taking the maximum. However, this is a pretty expensive way to do things - you're calculating 8.7k heights just to calculate a single maximum, and the calculations themselves are not particularly cheap. This quickly becomes a problem if you want to calculate a lot of locations.
Annual maximum tide is not the same year to year, and from memory, the tides have a long-term cyclic nature of around 18 years (that is the lowest common multiple of the periods of all of the cyclic components).
Is there a way of either analytically calculate the maximum tide height on a given day, or for a given year; or to calculate/estimate the time of that maximum (from which it would be possible to calculate the height)?
I'm only interested in the long-term predictable component of tides - astronomical tides (and perhaps other things, like local orographic effects?). Not interested in storm surge or wave effects, or other things that are hard to predict in the long term.