Reply to comment by C. Wunsch on ‘Wind stress forcing of the North Sea “Pole Tide” ’

(1) The quality factor Q is of course a fundamental property of a resonance in a transfer function characterizing its energy dissipation rate. Our conclusion in O2000 is that the observed 14-month periodicity in the North Sea tide gauge data is simply a result of the same periodicity that exists in the driving wind stress field in that region, and so there is no need to invoke any (14-month period) resonance behaviour in the transfer function for the North Sea. This same conclusion was reached by Tsimplis et al. (1994). For the sake of argument, let us assume there is such a resonance in the North Sea transfer function. Then Prof. Wunsch’s comment in principle points to a way to ‘test’ the phenomenon. However, the numerical approach he suggested (his Fig. 1) is not applicable in the present case. First, the width of the Fourier spectral peak is only a poor estimator for Q, because of the presence of the ‘natural’ spectral width (due simply to the finite recordlength) and spectral leakage problems. There are more sophisticated spectral methods that can yield better Q estimates, for example that based on Prony’s method (Chao & Gilbert 1980), or even the maximum-entropy/autoregressive spectrum (contrary to Prof. Wunsch’s comment; see Chao 1990). However, the real reason such estimators do not apply here is that they only apply to freely decaying (growing) sinusoids where Q is inversely proportional to the exponential decay (growth) rate, for example, the Earth’s free oscillational modes excited by a large earthquake (Chao & Gilbert 1980). For a continually excited resonance (in the sense that the intervals between excitations are shorter than the natural decay time of the free oscillation), it is no longer straightfoward to estimate Q numerically without actually knowing the excitation function. That is the case, for example, in estimating the Q of the Chandler wobble resonance (e.g. Furuya & Chao 1996), which is known to be continually excited. This would also be true in the present case, assuming that the 14-month periodicity is a resonance. Incidentally, we applied the maximum-entropy spectrum to the driving wind field in a careful manner, knowing its occasional instability as Prof. Wunsch pointed out. Nearly the same spectra were found for all individual NCEP data wind points in the area studied (only their average is shown in Fig. 2 of O2000). Furthermore, we did compute the (robust) multitaper Fourier spectrum for the wind field: it shows the same phenomenon where east–west winds show a spectrum very similar to Fig. 9 of O2000, while north–south winds have little power except at the annual period. (2) We agree with Prof. Wunsch’s statement that O2000 raised ‘an even more difficult problem than the one it solves’. That is, if there is no 14-month resonance in the North Sea transfer function, then the problem becomes how to explain the existence of the periodicity in the regional wind field in the first place, as ‘no such narrow-band process has ever been found in the atmosphere’. We have no insight as to why that is so; we simply adopted the wind field output data from the NCEP reanalysis and ‘ran with it’. However, one does realise that the North Sea wind field is presumably part of the North Atlantic Oscillation, which in turn has been recently recognized as an integral part of a bigger meteorological system known as the Arctic Oscillation. Finally, we do want to point out that this particular 14-month periodicity probably would not have attracted so much attention if not for its coincidence with the Chandler period. After all, there are other, equally prominent (non-seasonal) periodicities present in, for example, Figs 2 and 9 of O2000.