The astronomical tide
Forty-nine millimetres
At Constanța, between consecutive extremes, a two-hundred-year prediction rises 49.5 mm on average. At Cape d'Or, in the Bay of Fundy, the same Moon lifts 10.11 metres: 204.2 times the range on the Romanian shore.
The Moon is the same
The force that lifts the ocean is global. Basins answer differently. The Bay of Fundy has a natural slosh close to 12.4 hours, the Moon's semidiurnal period, and the water piles toward the Minas Basin like a trough. The Black Sea is nearly closed, small against the ocean, and the tidal wave that squeezes through the Bosphorus stays weak. The oscillation is born mostly inside the basin, from direct forcing, and it stays palm-sized.
In the global table of 4,907 tide gauges, built on the TICON-4 harmonic constants, Constanța has a mean of 49.5 mm between consecutive extremes. Mangalia, 49.0 mm. At Kacha, on the Crimean shore, the mean falls to 8.9 mm. Marseille, another enclosed sea, reaches 14.5 cm. Cape d'Or holds the table's absolute peak: 16.72 metres between two extremes, a mean of 10.11 metres.
Pick a harbour
The staff on the right is 16.72 metres, the table maximum. Pick a harbour. The water climbs only as far as that harbour's range. At Constanța it remains a film at the bottom. Move the hour through a 12.4-hour lunar semidiurnal cycle and watch the schematic level.
The curve is a cosine at the published amplitude, drawn for scale. Spring tides use the maximum from the same table.
Pick a harbour. The staff stays 16.72 metres.
Wind covers the palm
On the beach at Mamaia, the water retreats after a north wind and returns with the breeze. The astronomical oscillation of 49.5 mm sits under the waves and the seiche. A life on the Black Sea can pass without ever seeing the tide, though the Moon pulls here as hard as at Cape d'Or. The basin makes the difference.
The ratio of 204.2 is the two mean consecutive ranges: 10.11 metres divided by 49.5 mm. The maxima in the same table sit in a ratio of 141.7: 16.72 metres at Cape d'Or, 11.8 cm at Constanța. Both comparisons use the same operation, on the same columns.
A palm, a building
Forty-nine millimetres fit between thumb and forefinger. Ten metres are a three-storey building. The same Moon writes both marks. The staff holds them on one scale.
How to read the staff
Reading
The heights come from 200-year predictions (1900–2100) computed by Hart-Davis, Sulzbach and Talke from the TICON-4 harmonic constants, themselves derived from GESLA-4 records. Mean range is the average difference between consecutive extremes; the maximum is the largest such difference across those two centuries. The original unit is the millimetre. The 22 harbours on the staff are an extract from 4,907 stations. Constanța is the IOC/CMEMS station ioc_csta2 (44.147° N, 28.672° E). The prediction is astronomical: wind, pressure and seiche, which at Constanța can move the water by tens of centimetres, stay outside the mark. The staff on this page reconstructs a cosine with the M2 period at the published amplitude, as a scale, beside the sailing almanac.