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A Unified Analysis of Tides and Surges Round North and East Britain

D. E. Cartwright
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 263, No. 1134 (Apr. 4, 1968), pp. 1-55
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/73589
Page Count: 55
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A Unified Analysis of Tides and Surges Round North and East Britain
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Abstract

Tide gauge records from six ports round north and east Britain are analysed in terms of the response of sea level to gravitational and radiational tide potentials, and to a six-component function which describes the major features of the weather over the relevant sea area. Tidal interaction effects due to shallow water are allowed for up to third order. The linear tidal admittances in species 1, 2 and 3 are found to be smooth and consistent from one port to another. The radiational components are found to have amplitudes around 18% of the 12 h tide due to gravity at all ports, with consistent phase leads on the gravitational tide. The second-order interactions producing tides of species 4 are found to have strong dependence on frequency, and are surprisingly noisy at Southend. The third-order tides at species 6 have neither of these properties, and their amplitudes are shown to vary approximately with the cube of the main tidal amplitude. This last fact is reconciled with a quadratic frictional law. On the whole, the response analysis of the tides is found to be more accurate than a harmonic analysis which uses a greater number of arbitrary constants, with an increasing improvement in predictable variance at the shallower ports. At the two estuarine ports, effects coherent with interaction between tides and random variations in local sea level are found by a bispectral analysis. The interaction coefficients are reasonably consistent with those derived from the tides alone, and with computations by G. W. Lennon of wave propagation in the Thames Estuary. The interaction with local sea level is insufficient to account for the tidal modulations with frequencies less than 1 cycle/month. The spectra of these modulations at the M2 frequency ± f are strongly coherent, and show similar proportions of phase-and amplitude-modulations at all stations. They may be due to oceanic, local, or instrumental effects. The seasonal effects at f = ± 1 cycle/year stand out clearly, and point to a third distinct agent of tidal modulation. The functions chosen to describe the weather are the first six coefficients of a special Taylor expansion of atmospheric pressure. As well as describing the field of normal stress, these functions implicitly embody a linearized wind stress through the pressure gradients. Inter-correlation between the six components are allowed for. They are all found to give significant contributions to sea level variance, and their responses extend to at least 24 h time delay. An array of three stations, Malin Head, Stornoway and Lerwick, is tested for detecting `external surges' arriving as free waves at Aberdeen, but only Stornoway is found to be usable from the point of view of prediction. Self-prediction of consistent (low frequency and tidal) errors in the prediction of sea level by other variables is shown to be effective and useful. Finally, the noise level in low frequency sea level is reduced by subtracting its purely weather-dependent part, to reveal significant values of the monthly and fortnightly tides. Their amplitudes are found to be surprisingly large (ratios of order 1) in relation to the zonal equilibrium tide.

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