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.

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    $\begingroup$ Is it possible that these turbines are designed for a life-time of 25 years, so the bolded statement simply tells us that once deployed, their energy output can be predicted accurately over their entire life-time? $\endgroup$ – njuffa Mar 18 '19 at 6:06
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    $\begingroup$ the only thing one need to calculate the tides into the future is the sun and the moon,it does not matter if it is 10 years or 10000 years.you can take a look here to find more information about the sun and the moon timeanddate.com $\endgroup$ – trond hansen Mar 18 '19 at 7:31
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    $\begingroup$ @trondhansen I haven't asked about predicting high tide tables, I've asked about the speed and volume of sub-surface currents off of coastal areas that would run turbines. how about precession of the poles, sea level changes, ocean temperature changes, or climate in general? If you are sure neither these nor anything else can have no significant impact (which could certainly be true) then feel free to post an answer, thanks! $\endgroup$ – uhoh Mar 18 '19 at 7:37
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    $\begingroup$ i do not think it is possible to give an accurate forecast for how the ocean curents and the weather will develop 25+years into the future. $\endgroup$ – trond hansen Mar 18 '19 at 7:56
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    $\begingroup$ @trondhansen - Predicting the tides has little to do with weather. Weather is intentionally averaged out in creating tide prediction tables. $\endgroup$ – David Hammen Mar 18 '19 at 10:33

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.

  • $\begingroup$ Thanks, I had a hunch you might chime in. On the scale of 25 years, off the coast of northern Scotland, any thoughts on which ones are likely to be the most important? $\endgroup$ – uhoh Mar 18 '19 at 12:50
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    $\begingroup$ @uhoh - I would suspect the noisiness, the things tidal models cannot predict. Another factor is that the North Atlantic is where a good portion of the world's tidal energy dissipates. Some of this dissipation will show itself as even more noise. $\endgroup$ – David Hammen Mar 18 '19 at 12:55
  • $\begingroup$ Thanks, I see what you mean. btw I'm not sure if you are up for some Space Chemistry, but What gas was produced in orbit from 33 pounds of benzoic acid and anthraquinone? $\endgroup$ – uhoh Mar 18 '19 at 12:56
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    $\begingroup$ @DavidHammen, tidal energy dissipation is what gives the structure of the tides we see. The position of amphidromic points, the magnitude and phase at a specific location are determined by frictional dissipation and there is no noise associated with it. As with any harmonic analysis, the addition of more constituents helps constrain the fit. The noise in the water level signal is the fact that tides interact with any other forcing both linearly and non-linearly. We can definitely predict the tides much better than any other oceanic signal. The issues are resolution and parameters like friction $\endgroup$ – arkaia Mar 21 '19 at 15:47
  • $\begingroup$ I agree with your comment but disagree with the statement that the method is not an analytical science. In many areas of earth science, models calibrated to known data and verified against new data are used for prediction. The physical basis for the model can be incompletely known but it is still scientifically valid. $\endgroup$ – haresfur Mar 25 '19 at 23:31

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.

  • $\begingroup$ A comment regarding "flow velocities" (tidal currents). They are much more complicated than tide levels, as noted, but they can be quite accurately predicted in terms of direction and relative strength, even in complicated shoreline areas by relating known values to the moon phase and seasonal relationships. See charts.gc.ca/publications/atlas-eng.asp $\endgroup$ – haresfur Mar 25 '19 at 23:25

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