The Angry Corrie 48: Jan-Feb 2001

TAC 48 Index

Too low for zero (sea level saga)

Grant Hutchison

In an odd coincidence, Chris Pearson and Paul Hesp both recently wrote letters (TAC47, pp17-18) making reference to the idea that sea level was higher in some places than others. But hang on a minute - higher relative to what, exactly? We measure height from sea level, after all. Saying that sea level in Scotland is lower than in England is like saying that the value of zero falls slightly once you've driven north of Gretna. No doubt mono-literate folk like Gordon Smith could cheerfully weave an ironic metaphor around that notion, but those of us who speak both English and mathematics develop a sort of existential vertigo. The value of zero varies from place to place...

Well, not exactly. It's all got to do with the shape of the Earth. To a first approximation the Earth is an ellipsoid, slightly flattened at the poles. Cartographers hug that simple shape to their mathematical bosoms, because it makes their map projection sums easier. And if the Earth were just a homogenous lump of basalt with the oceans poured on top, sea level really would conform perfectly to the cartographers' ideal ellipsoid. But the real Earth is a sort of geological plum duff, denser in some places than others. So it's gravitationally lumpy, and sea level accommodates itself smoothly to that varying gravitational field - bulging here and there to form "hills" a few tens of metres high and a few thousand kilometres across. The cartographers' simplistic ellipsoid can only approximate the real shape of the ocean surface. The seas around the UK actually sit about 55m above the overall- best-fit ellipsoid - a couple of metres higher in the west, a couple lower in the east. So the Ordnance Survey have used (until recently) a slightly different ellipsoid that specifically fits UK sea levels better - the mysterious "Airy Spheroid" that still features in the margin of your OS maps. The US also defined their own national ellipsoid. In fact, at least 25 "standard" ellipsoids have been concocted by cartographers to fit various parts of our lumpy globe more or less accurately. And that gives the game away - if you talk about sea level's "height" relative to an ellipsoid, you're getting things the wrong way round. Sea level is the zero datum, and the various ellipsoids are just mathematical contriv-ances to help the cartographers get home from the office at a reasonable time.

The OS haven't actually measured mean sea level everywhere in Britain - instead they laid out a huge network of bench marks using sightings and spirit levels, all zeroed against the mean sea level recorded at Newlyn between 1915 and 1921. If you imagine real sea level as a smooth, imperceptibly billowy surface, then the OS have approx-imated that with a set of straight sight-lines connecting their various bench marks. There's a source of error there, which could mean that sea level somewhere in the country turns out to be a tad higher or lower than the OS's zero level. The heights of mountains measured from the OS datum would therefore be different from their true height above local sea level. But as David Purchase once suggested (TAC42, pp10-11), the error is small - no more than 20cm over the length of the country.

Something called "sea surface topography" causes real differences in sea level from place to place, although these differences may vary depend-ing on when you measure them and over how long you average your measurements. For instance, a body of unusually cold salty water will be unusually dense, too - it will settle a little lower than a neighbouring area of warm water, just like two people of different weights sitting on a water bed. Onshore currents can create a slight bulge in the local sea surface, as can onshore winds; and areas with lower-than-average barometric pressure end up with a higher sea level (by about one centi-metre per millibar). The UK sits at the bottom of a more-or-less permanent 80cm valley in sea surface topography, and there are smaller variations from place to place around the coast.

So sea surface topography alone isn't going to help Chris Pearson in his quest for a tidal Marilyn. His best candidate is the 146m island of Seil, with a spring tide range of 4.5m - that's a 2.25m drop at low tide, but the waters would need to recede by at least four metres to give Seil the necessary 150m of ascent for temporary Marilyn status. The other, lower, island SubMarilyns look like no-hopers in this regard - Soay, Tiree and Colonsay sit in open sea areas with (I estimate) only a couple of metres of tidal range. Lundy is in the middle of the whopping tidal flow of the Bristol Channel, with a spring tide range of eight metres - but the island is only 142m high, and so would need double that range to give it tidal Marilyn status.

And there's a real possibility that, even if the Atlantic withdrew right off the continental shelf, Seil still might not turn into a Marilyn - the narrow Clachan Sound separating the island from the mainland is barely navigable at high tide, and reced-ing waters might reveal nothing but a rocky valley 149m below Seil's highest point, Meall a'Chaise. But for now let's assume Clachan Sound harbours a cleft at least four metres below present sea level, and see where we can go from there.

Not all spring tides are the same height. They occur twice a month when the gravitational pulls of the moon and sun align with each other, but the alignment is rarely exact, because the moon's orbit around the Earth is inclined at five degrees to the Earth's orbit around the sun. For high spring tides we want an exact alignment, which only occurs at the time of a lunar or solar eclipse. We'd also like the Earth to be at its closest to the sun, to get the maximum effect from solar gravity. At present that closest approach happens in early January, and there are correspondingly higher spring tides around New Year - Australians call them "king tides". And finally we'd like the moon to be at its closest to the Earth, too, to get the most effect from its gravity. The high spring tides during close lunar approaches are called "perigean springs". Put them all together and you have the highest possible tide - a "king perigean eclipse tide" (to coin a phrase). Tides are tricky things, but it's possible such an event could increase the normal spring tide range by as much as 40%. In the case of Seil, that would push low tide down to ... (damn) 3.15m.

Can sea surface topography buy us the extra 85cm? Well, remember we get a one-centimetre change in sea level for each millibar of atmospheric pressure - all we'd need would be some high pressure to push sea level down, and a few days for the sea to equilibrate. The highest atmospheric pressure ever recorded is 1084mb, in Siberia, during December 1968. Normal pressure is 1013mb, so that's ... (damn) 71cm of sea-level depression.

Still fourteen tantalising centimetres short. Apart from dumping a very large quantity of cold salt water into the Firth of Lorn, there's not a lot more I can suggest except the introduction of a hurricane force offshore wind. Not common during stable high pressure, I know, but these are desperate times.

So: if the next king perigean eclipse tide coincides with a prolonged period of Arctic high pressure and some implausibly brisk anticyclonic winds, I'll meet you on Seil. We'll be the first folk to bag a tidal Marilyn, since I'm sure no-one bothered during the last mega-tide on 28 December 1712. So mark your diary: the next big one is due on ... (damn) 18 January 3089.

Sod it. Sea level will have risen by then.

TAC 48 Index