Introduction
Many different types of tide gauge are now in use around the world. These include traditional float and stilling well gauges (Noye, 1974a,b,c; IOC, 1985; Pugh, 1987), acoustic gauges (Gill and Mero, 1990) and gauges based on the principle of measuring sub-surface pressure (Pugh, 1972). Pressure tide gauges are more convenient to use than others, especially in environmentally hostile areas, but their data are often difficult to relate to a land datum to better than a few centimetres. Methods used at present to impose a datum on pressure time series include simultaneous measurements at a nearby stilling well; tide poles or stilling tubes and observers; water level 'switches' in mini-stilling wells; and the use of 'comparators', or precisely calibrated reference pressure devices. Each of these has drawbacks.
The stilling well method probably produces usable results, as long as comparisons are performed over several complete tidal cycles to remove the effect of any lag in the well. However, a stilling well will not always be present and it will have its own systematic error sources (Lennon, 1971). A tide pole is very tedious for the observer and is useful only for first order checks in calm conditions. Switches show great promise and it is possible that reliable switch systems may eventually be developed. However, present ones do not entirely eliminate the effect of waves, even given the mini-stilling wells, and they are probably accurate to only a few centimetres, which is not good enough for long term recording. They also tend to foul in the dirty water often present in harbours. Finally, although the comparators used routinely by the UK Tide Gauge Inspectorate (UK TGI) appear to provide datum control of centimetre accuracy or better, they do not provide a near-continuous datum check, are clumsy to operate and are not well documented (CTG, 1986).
Pressure tide gauges already comprise a major subset of those in the GLOSS (Global Sea Level Observing System) network (IOC, 1990) and provide the best form of instrumentation for extending the network to environmentally hostile areas (IOC, 1988). Therefore, it is clear that a simple method is required to provide precise and near-continuous datum control to the time series from pressure gauges.
A method has been developed at POL for the precise datum control of sea level records from pressure tide gauges. By means of an additional pressure point at approximately mean sea level, it has been found that an effective temporal discrimination of the sea level record can be used to impose a datum upon itself. Two experiments, one based on bubbler gauge technology and one on pressure transducers installed directly in the sea, have demonstrated that the method is capable of providing millimetric precision datum control.
A Brief Description of the Method
A schematic pressure gauge setup is shown in Figure 1 with a pressure sensor in the water ('C') and another in the atmosphere ('A'). Around the UK national tide gauge network (called the 'A Class' network), the pressure difference C-A is usually recorded in a single channel of a differential transducer connected to a bubbler gauge (Pugh, 1972). At the South Atlantic sites of POL's ACCLAIM (Antarctic Circumpolar Current Levels by Altimetry and Island Measurements) network, C and A are separate absolute transducer channels (Spencer et al., 1993). In both cases, Paroscientific digiquartz sensors are employed (Banaszek, 1985). It is the difference C-A which gives sea level, after sea water density correction, and which must be constrained to a land datum. In practice, both C and A, or their difference, may measure pressure changes extremely well, but it would be common for their data to contain uncalibrated offset pressures and small low-frequency drifts specific to each individual pressure transducer. In addition, other parts of the apparatus may also introduce biases and drifts (e.g. through insufficient gas flow in a bubbler gauge) or the ocean itself may drift (i.e. through density changes).
In the present experiment, another pressure gauge 'B' is placed at 'datum B' (Figure 1) which is a datum approximately at mean sea level. Datum B would be geodetically connected to the local levelling network (Carter et al., 1989) and, it will be seen, will supply a sort of Tide Gauge Zero. The essential feature is that, while any pressure measured by a sensor at B will also contain an offset, and maybe a drift, the vertical height of its effective pressure point can be positioned at datum B very accurately. So, although it is not known absolutely HOW MUCH it is measuring to within perhaps a few mbar (i.e. to within a few cm), it is known WHERE it is measuring it to millimetric precision.
Figure 2 demonstrates schematically the idea behind our method. Figure 2(a) shows the C-A record while Figure 2(b) shows the B-A record with the assumption of no waves. Initially, the datum of each record will be unknown. Of course, the latter is the same shape as the former, except that as the still water level drops below datum B the curve of Figure 2(b) bottoms out generating an inflexion point at the steepest part of the tidal curve at times 't1' etc. The flat part of B-A and its inflexion points will provide an extremely precisely defined shape which will be immune to any problems with datum offsets and low-frequency instrumental drifts. Our computation now involves overlaying the full curve of Figure 2(a) on to 2(b) using the top parts of the tidal cycles. Then the intersection of the flat line with the full curve can easily be computed, and the corresponding C-A values redefined to be at datum B. In other words, the datum has been transferred.
What about a more realistic situation with waves? Figure 2(c) shows that the sharp inflexion points might become rounded by waves, and it will not be until the wave crests have fallen with the tide below datum B that the curve will bottom out properly. However, this should not be a problem, provided that the waves are not too large, as Figure 2(c) can still be matched with 2(a) with the flat bit extrapolated on to the full curve. In practice, the matching can easily be done by least squares fit with a software algorithm designed to leave the area of the rounded inflexion points out of the computation.
This procedure is analogous to the function of the mechanical and acoustic water level switches used by the UK TGI. However, a switch acts at an instant and may go off prematurely with waves around. The 'software switch' here is the several hours of the bottom- out of B-A and is, in effect, a time-averaged discrimination of C-A. The rounding of the inflexion points due to waves will not bother the method in general but, as we are interested here in using B to establish a datum at regular intervals, rather than obtaining a continuous time series, the data of high wave days can simply be ignored. (Obviously we want a continuous record from C-A). High wave conditions might be identified from the degree of rounding at the inflexion points, or the digiquartz of C could be made to record at 1 Hz or higher frequency to measure them. 'B recording' may be intermittent at some sites owing to environmental or operational restrictions, and recording could be a feature of visits to remote islands or summer stays at polar bases. In our experience, such a procedure might be adequate to provide long term datum control to a continuous C-A record, as long as good (i.e. previously tested, relatively stable) transducers were used and the visits were at least once every year. However, where possible, it would be desirable to have the B sensor installed permanently as there is great appeal in being able to check the datum with every low tide (i.e. twice a day in most places).
In order to work properly, the method obviously needs a sizable tidal range so that B will be half the time in water and half the time in air. It will not work in lakes or microtidal areas but most coastal and many island sites have usable tidal ranges, even if only at springs. Clearly, 'tide' here means any real signal. 'Surge' will do quite as well as long as the same signal is observed in the top halves of B-A and C-A to enable them to match up. The method does not require the actual installed height of C or A to be known. Where it is difficult to install a fixed gauge C below the water, because of shallow gradients perhaps, then a pop-up, or bottom mounted and diver replaced gauge, could be used. Example locations where this might apply include the Tropical Atlantic, where POL and French groups have operated such gauges for several years, and Heard and Macquarie Islands, where the University of Flinders has made similar measurements. In fact, the height of A should be kept constant, with its readings compared regularly to a precise barometer, but that is for meteorological data purposes, not tide gauge considerations.
What do we expect the accuracy of the method to be? That depends on how flat the bottoming-out of B-A is. If completely flat, the method is theoretically perfect but there will be systematic errors depending on the hardware. Fifteen minute or higher frequency sampling would be better than hourly heights in order to clearly resolve the inflexion points but, whatever the sampling, it is important for A, B and C to record pressure simultaneously and in a similar fashion.
To summarise, the most important feature of the method is its ability to impose a datum as a function of time and its ability to handle slow drifts in any, or all, of the A, B and C transducers. As any drifts will manifest themselves as changes in the vertical conversion factor to impose the curve of Figure 2(b) on to that of Figure 2(a), they can be continuously adjusted for by constant constraint of C-A to the B datum imposed by the least squares adjustment.
Experimental Results
In brief, the method has been shown to work well in two experiments at Holyhead (where the mean tidal range is 3.6m) using both bubbler and digiquartz-in-the-sea systems. An internal POL report (Smith et al., 1991), from which the above sections were extracted, gives further details and has been circulated to members of the GLOSS Experts group and to a number of tide gauge authorities. Additional copies may be obtained from the PSMSL.
Since the 1991 Holyhead experiments, purpose built equipment based on the same principle has been constructed for the digiquartz-in-the-sea technique for use at South Atlantic sites where the mean range is typically 1 metre. Figure 3 shows the design of the gauge employed at Ascension and St.Helena. Gauges at Tristan da Cunha, Port Stanley and Rothera are adaptions of this basic design for the local requirements. Approximately six of the 'A Class' bubblers around the UK have also be modified along these lines so far. POL would be interested in working with any group which might be interested in jointly developing this technique.
References
Banaszek, A.D. 1985. Procedures and problems associated with the calibration and use of pressure sensors for sea level measurements. In, Advances in underwater technology and offshore engineering, 4, 103-127. (London: Graham and Trotman).
Carter, W.E., Aubrey, D.G., Baker, T.F., Boucher, C., Le Provost, C., Pugh, D.T., Peltier, W.R., Zumberge, M., Rapp, R.H., Schutz, R.E., Emery, K.O. and Enfield, D.B. 1989. Geodetic fixing of tide gauge bench marks. Woods Hole Oceanographic Institution Technical Report WHOI-89-31, 44pp.
Committee On Tide Gauges (CTG). 1986. Tide gauge requirements. Bidston, Merseyside: Committee on Tide Gauges, 22pp.
Gill, S.K. and Mero, T.N. 1990. Next generation water level measurement system: implementation into the NOAA National Water Level Observation Network. pp.133-146 in, Towards an integrated system for measuring long term changes in global sea level, (ed.H.F.Eden). (Report of a workshop held Woods Hole Oceanographic Institution, May 1990). Washington, DC.: Joint Oceanographic Institutions Inc. (JOI). 178pp. & appendix.
Intergovernmental Oceanographic Commission (IOC). 1985. Manual on sea level measurement and interpretation. Intergovernmental Oceanographic Commission, Manuals and Guides, No.14, 83pp.
Intergovernmental Oceanographic Commission (IOC). 1988. Workshop on sea-level measurements in hostile conditions, Bidston, UK, 28-31 March 1988. Summary report and submitted papers. Intergovernmental Oceanographic Commission, Workshop Report No.54, 81pp.
Intergovernmental Oceanographic Commission (IOC). 1990. Global Sea Level Observing System (GLOSS) implementation plan. Intergovernmental Oceanographic Commission, Technical Series, No. 35, 90pp.
Lennon, G.W. 1971. Sea level instrumentation, its limitations and the optimisation of the performance of conventional gauges in Great Britain. International Hydrographic Review, 48(2), 129-147.
Noye, B.J. 1974a. Tide-well systems I: some non-linear effects of the conventional tide well. Journal of Marine Research, 32(2), 129-135.
Noye, B.J. 1974b. Tide-well systems II: the frequency response of a linear tide-well system. Journal of Marine Research, 32(2), 155-181.
Noye, B.J. 1974c. Tide-well systems III: improved interpretation of tide-well records. Journal of Marine Research, 32(2), 193-194.
Pugh, D.T. 1972. The physics of pneumatic tide gauges. International Hydrographic Review, 49(2), 71-97.
Pugh, D.T. 1987. Tides, surges and mean sea-level: a handbook for engineers and scientists. Chichester: John Wiley and Sons, 472pp.
Smith, D.E., Spencer, R., Vassie, J.M. and Woodworth, P.L. 1991. Precise datum control for pressure sea level records. POL Internal Working Document.
Spencer, R., Foden, P.R., McGarry, C., Harrison, A.J., Vassie, J.M, Baker, T.F., Smithson, M.J., Harangozo, S.A. and Woodworth, P.L. 1993. The ACCLAIM Programme in the South Atlantic and Southern Oceans. International Hydrographic Review, 70, 7-21.
Figure Captions
1. Schematic illustration of a pressure gauge setup containing three pressure transducers: an 'A gauge', which measures atmospheric pressure; a 'C gauge' which measures sea pressure; and a 'B gauge' placed at approximately mean sea level.
2. Schematic illustrations of (a) the tidal curve produced from the C-A pressure time series; (b) the ideal B-A time series showing inflexion points 't1' and 't2'; (c) the B-A time series possibly distorted by the presence of waves.
3. Schematic drawing of the half-tide tide gauge system at Ascension Island.
This article is adapted from a section of the report of the "Joint IAPSO-IOC Workshop on Sea Level Measurements and Quality Control, Paris, 12-13 October 1992. Intergovernmental Oceanographic Commission Workshop Report No.81, 167pp, edited by N.E. Spencer". A longer version of the article is in: Woodworth, P.L., Vassie, J.M., Spencer, R. and Smith, D.E. 1996. Precise datum control for pressure tide gauges. Marine Geodesy, 19(1), 1-20.
