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 designate the tide producing forces, the spike response and the predicted 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 / from a station record (using capitals for Fourier transforms) and then predicting future from a Fourier transform of . | 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 predicted tide all referred to one particular tide station. Then the convolution integral gives the predicted tide z 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 modulation and hyper-fine splitting by the lunar year modulation. The discrete frequencies are not at equal intervals as in classical harmonic analysis but occur at fijk c cpd Cjcpm ckcpy . 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 response 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 station 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 improvement was substantial. Hasselmann How about shallow regions with strong overtides Munk That is an important point. For very flat .
