Oceanography

Tidal predictions

Astronomical tides do not include weather effects. Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.) away from those prevailing at the measurement time affect the tide's actual timing and magnitude.  Organisations quoting a "highest astronomical tide" for some locatin may exaggerate the figure as a safety factor against analytical uncertainties, distance from the nearest measurement points, changes since the last observation time, ground subsidence, etc, to avert liability should an engineering work be overtopped.  Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide form the observed tide.

                             

      Careful Fourier data analysis over a nineteen-year perid (teh national Tidal Datum Epoch in the U.S) uses frequencies called teh tidal harmonic constituents.  Nineteen years is preferred because 19 years, which is long enough to include the 18.613 year lunar nodal tidal constituent.  This analysis can be done using obnly the knowledge of the forcing period, but without detailed understanding of the mathematical derivation, which means that usefull tidal tables have been constructed for centuries.  The resulting amplitudes and phases can then be used to predict the expected tides.  These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day or fortnightly, monthly, and semiannual.  Seidiurnal tide dominated coastline, but some areas such as the south china sea and the Gulf of Mexico are primarily diurnal.  In the semidiurnal areas, teh primary constituents M₂ (lunar) and s₂ (solar)periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period). In the M₂ plot above, each cotidal line differs by one hour form its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.  The lines rotate around the amphidromic points counterclockwise in the northern hemisphere so that form Baja California peninsula to Alaska and from france to ireland the  M₂ tide propagates northward.  In the southern hemisphere this direction is clockiwise. On the other hand M₂ tide propagates counterclockwise around New Zealand, but this is because the islands act as a dam and permit the tides to have different heights on the islands opposite sides. (The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.)

  the exception is at cook strait where the tidal currents periodically link high to low water.  This is because cotidal lines 1800 around the amphidromes are in opposite phase, for example high water across from low water at each end of cook strair.  Each tidal constituent has a different patternof amplitudes, phases, and amphidromic points, so the M₂ patterns cannot be used for other tide components.

example calculation

Further information:  The article onA.T. Doodson has a fully-worked example calculation for Bridgeport, connecticut, U.S.A.

      Figure 2 shows the commn pattern of two tidal peaks a day as the earth rotates under the moon because the moon is also moving in its orbit around the earth and in the same sense as the Earth's rotation, a points on the earth must rotate slightly further to catch up so that the cycle time is nt twelve but 12.4206 hours a bit over twenty-five minute extra.  The two peaks are not equal the twin tidal bulges beneath the Moon and on the opposite side of the earth align with the moon.  Bridgeport, bridgeport is closer to its maximum tide than approximately twelve hours later when bridgeport is on the opposite side of the earth form the moon and the high tide bulge at bridgeport's longitude has its maximum south of the equator.  Thus the two high tides a day alternated in maximum heghts lower high (just under three feet), higher high (just over three feet), and again. Likewise for the low tides.

   Figure 3 shows the spring tide/neap tide cycle in tidal amplitudes as the moon orbits the earth form being in line (sun-earth-moon, or sun-moo -earth) when the two main influences combine to give the spring tides, to when the two forces are opposing each other as when the angle moon-earth-sun is close to ninety degrees, producing the neap tides.  As the moon moves around its orbit it changes from north of the equator to south of the equator.  The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the moon is above the equator), then redevelops but with the other polarity, waxing to a maximum difference and then waning again.