What goes into a tide power prediction for every fifteen minutes over the next twenty five years?

Question

I was watching a segment about tidal power generation on a PBS NewsHour broadcast. I've set the time code at about 11:45 to capture a little background. This bit starts at 12:36:

As the tide ebs and flows, the turbines spin between seven and fifteen times a minute, generating power similar to a wind turbine. Cables cary the energy back to shore; first underwater, then underground, where it’s then fed into the national grid.

The tides are so predictable that Atlantis says it can tell how much energy these turbines will generate every fifteen minutes for the next twenty-five years.

What kind of information goes into such a long-term prediction? Is it just the relative positions of the Sun, Earth, and Moon, or something more? I ask because those positions can be calculated for thousands of years, there wouldn't be a cut off at only 25 years, so I assume there's more that goes into it.

Answer 1

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.

Answer 2

As another answer has stated, tides can broadly be predicted far ahead by harmonic analysis (which is similar to taking a fourier transform of the tidal signal, but only allowing frequencies that correspond to various astronomical periods of the sun, the moon, and interactions between the two).

There are some caveats to this.

• As David Hammen has noted, water depths may change over time due to changes in sediment. In many of the tidal sites that are currently being developed the speed of the current means that the seabed is scoured rock, without sediment, but in some areas this change may nevertheless become significant, perhaps over a 25-year timescale.

• Superimposed on this astronomical signal can be significant (up to approx. 0.5 m/s) short-term variations due to meteorological effects such as surface winds and storm surges. This limits the accuracy with which one can predict the speed of tidal flow more than a few days ahead, but does not give a rationale for the 25-year figure.

• As noted by this paper and others, while the astronomical (rather than meteorological) component of water elevations resulting from tides can be fully described using a sufficient number of harmonic constituents, the same is not always true of flow velocities. This is because the shape of landforms and of the seabed can cause additional periodic changes in the velocity at a given location which do not correspond to astronomical frequencies. An example is the tendency of a "jet" to form downstream of a constriction at certain phases of the tide. Nevertheless, harmonic analysis can still usually provide a close approximation and, once again, this does not provide a rationale for the 25-year limit given.

I suspect that 25 years is simply a number plucked from the air to mean "a long time", perhaps informed (as noted in a comment) by that being the intended lifetime of the turbines.