Seventy Years of Exploration in Oceanography Part 5 pptx

42 6 Deep Sea Tides 1964–2000

Munk: Cartwright and I proposed what we thought was a significant change in

the method of tide prediction [97]. I will need to write a bit of mathematics. Let

x.t / designate the tide producing forces, y.t / the spike response and z.t / the pre￾dicted tide, all referred to one particular tide station. Then the convolution integral

gives the predicted tide, z D x y. The harmonic method consists of evaluating the

station tide spectrum Z.f / from a station record z.t / (using capitals for Fourier

transforms) and then predicting future z.t / from a Fourier transform of Z.f /. The

trouble is that Z.f / is very complex, with the principal diurnal and semidiurnal

lines split by monthly modulation, with further fine splitting by the annual modula￾tion and hyper-fine splitting by the lunar 18.6 year modulation.

The discrete frequencies are not at equal intervals (as in classical harmonic analy￾sis) but occur at fijk D ci cpd C cj cpm C ckcpy C ::: where the c’s are integral

multipliers of the daily, monthly and yearly frequencies. Weak lines are improperly

enhanced by including some of the noise continuum. There is no reference to the

gravitational theory of tides (except for providing the fijk frequencies). In the re￾sponse method we evaluate the tide producing forces x.t / directly from the known

motions of Earth, Moon and Sun in the time-domain, and then use the station record

z.t / to evaluate the station response y.t / once and for all. It turns out that the sta￾tion admittance Y .f / is vastly simpler than X.f /; there is no need of evaluating the

infinitely complex spectrum X.f / or Z.f /. In some tests by Zetler et al. [123] the

response method come out better (but only slightly) than the harmonic method.

Hasselmann: So you improved one of the few geophysical predictions that already

work well.

Munk: Guilty. But for very short records (such as the deep-sea recordings) the im￾provement was substantial.

Hasselmann: How about shallow regions with strong “overtides”?

Munk: That is an important point. For very flat shelves with strong nonlinear in￾teractions the response method can easily be extended by a formalism parallel to

extending a spectrum to a bi-spectrum. . .

Hasselmann: I see. Tukey again to the rescue – although I guess the use of nonlinear

response function expansions in the time domain probably preceded their applica￾tion in the frequency domain.

Munk: Perhaps, we at any rate were happy to work in either the frequency domain

or time domain, whichever was more efficient for the problem at hand. Essentially

what the response method does is to keep an open mind on what side of the Fourier

transform is more compact. The three-body problem Earth-Moon-Sun has an ex￾ceedingly complex spectrum and the time domain is the domain of choice; if our

world were associated with two-body tides (double-star without moons) it could be

the other way around, the harmonic method would be the method of choice.