Providing a Levelling Datum to a Tide Gauge Sea Level Record

Abstract

A method is described for providing a levelling datum to a sea level record containing hourly heights (or similar) with the use of a second record from a nearby location consisting of high waters only but measured to a known datum. The method is tested using data from a pair of stations in the Thames estuary where there is a predominantly semidiurnal tide. It is then applied to the determination of a datum for an important historical sea level record at Liverpool. The historical background to that important record is explained. The limitations of the method are investigated using data from a pair of stations approximately 50 km apart on the north coast of Wales. This latter case study provides insight into which aspects of the tide contribute to inaccuracies in the method when the stations are some distance apart.

Keywords:

• Datum determination
• high water level variations
• historical sea level change at Liverpool
• ocean tidal constituents

Acknowledgements

Peter Hogarth is thanked for the information on Liverpool MSL in Figure 3. Some figures were generated using the Generic Mapping Tools (Wessel and Smith 1998).

Disclosure statement

No potential conflict of interest was reported by the author.

Data availability statement

All tide gauge data discussed in this paper can be obtained from the British Oceanographic Data Centre (https://www.bodc.ac.uk).

Notes

1 The tidal form factor is defined by the sum of the amplitudes of the O1 and K1 constituents divided by the sum of the amplitudes of M2 and S2. A location with a form factor lower than 0.25 is normally considered to have a semidiurnal tidal regime (Pugh and Woodworth 2014).

2 Using the set of constituents discussed in Sec. 4, one can identify no less than 8 diurnal and 10 semidiurnal pairs of constituents which contribute to the 14.77 day cycle in HW.

3 HMTR will be slightly larger than the amplitude of M2. The ‘excess’ amount includes contributions from every other tidal constituent, as demonstrated in Doodson and Warburg (1941) and Appendix A of Woodworth et al. (1991). To the extent that about half of this excess arises from S2, it can be shown that the total HMTR at the two locations will be in the proportion α, just as the S2 and M2 amplitudes are assumed to be.

4 Sea levels will be expressed to one millimetre and slopes to four decimals. Equation (1) involves the term (α − 1) HMTR^F and HMTR^F is ∼200 cm at the Thames ports or ∼300 cm at Liverpool, so four decimals are needed to be within one millimetre.

5 One puzzle is that, if the tidal measurements had been made at the lighthouse itself, which dries out at low tide, then it would have been impossible to record the lower part of the tidal curve. However, Denham’s data show no evidence for such bottoming out. One possibility is that the measurements were in fact made by the lighthouse keepers at a wooden pier approximately 600 m from the lighthouse. Both locations would have been known locally as ‘the Rock Lighthouse’ as far as anyone was then concerned.

6 The only similar exercise that I know of is an unpublished study of inferring the datums of temporary tide gauge records in the Bristol Channel by using simultaneous high water levels at Avonmouth (David Pugh, private communication).