"Geologic" Tides.--Any change in shape of the ocean basins or in the total quantity of water in them can bring about changes of level at a given locality. Another effect, however, is to change the dynamical response of the oceans to the tide-genetating forces, and we should consequently expect the tidal harmonic "constants" to change.

The geological change in sea level is quite slow as compared to that effected by the moon and sun, and is manifested by a small year to year variation in mean annual sea level. There is evidence that the average sea level over the entire earth rose by the order of 10 cm. from 1850 to 1950. This has been related to a shrinking of the ice caps of the world, particularly those over Antarctica and Greenland. About 1000 B.C., during the postglacial temperature maximum, sea level probably stood about 5 in. above its present level. At the present time there are localities where the average annual sea level is rising and others where it is falling, and this is attributed to a relative downward or upward motion of the land area in the vicinity. The horizontal extent over which these year to year sea level records appear similar gives a good indication as to the size of the portions of the earth's crust that are sinking and rising. Actually, the similarity extends over many hundreds of kilometres, indicating that masses somewhat smaller than continents are moving as a whole.

Variation of the tidal harmonic "constants" by the processes just described is probably a slow process, and it may be doubted that a detectable change would occur within tens of thousands of years. At locations where the tidal constants depend critically on the local, small-scale topography, however, this is not the case. For example, the tide up a river may depend critically on the conditions of the channel at the river's mouth. At many ports the tide has changed noticeably after the construction of port facilities, such as breakwaters, etc. In such cases the altered regime of sedimentation and erosion of sand usually plays an important part. Also, sand bars can form and disappear quite rapidly, and a sernienclosed lagoon behind such a condition would experience variable tidal "constants."

Meteorologic Tides.--The principal meteorologic effects can be ascribed directly or indirectly to variations in atmospheric pressure on the sea surface, tangential stress on the sea surface exerted by the wind, heating and cooling of the sea water.

A varying atmospheric pressure acting on the oceans has the characteristic of a body force, as the pressure gradients are transmitted through the water practically simultaneously from the sea surface to the bottom. For this reason, the dynamical problem is formally equivalent to that concerned with the effect of the tide-generating forces on the oceans, and equations (1) and (2) are still valid provided that  is replaced by , p_a being the atmospheric pressure and  the water density.

Under certain circumstances the dynamical response of the ocean to the atmospheric pressure disturbance can become large. If a tidal basin is subjected to a variable atmospheric pressure disturbance acting periodically with a frequency near that of one of the free modes of oscillation of the basin, the amplitude of its response will tend to increase until it is ultimately limited by frictional dissipation. The same is true in the case of a pressure disturbance travelling across the sea surface with the same velocity as that of a long free wave, or . It may be noted that the depth of the open ocean is so great that storms seldom attain this critical velocity, and so such magnifying effects are more often encountered in shallow seas.

For a longer-period fluctuation the dynamical effects are less important, and under these conditions the ocean's response is similar to that of an inverted barometer. The sea surface is depressed approximately a centimetre for each millibar of pressure increase, and vice versa, according to the hydrostatic law

Pressure changes of 20 millibars occurring in a few days are common at many ports, and so it may be seen that this effect could be one of the principal sources of error in tidal predictions.

Wind blowing across the water surface exerts a horizontal stress on the water directed downwind, largely by virtue of the difference in air pressure on the lee and windward sides of the water waves generated by the same wind. An exact law for this stress as a function of wind speed has not yet been discovered, but the semi-empirical relationship

gives a good approximation. Here  is the wind stress,  the density of air, v the wind speed at an elevation of 15 m. above the water surface and  is a numerical constant for which the value 0.0026 gives the best fit to the empirical data.

Wind stress on the sea surface directed toward the coast has the effect of piling up water against the coast, raising the sea level. Longshore winds blowing so that the land lies to the right relative to the wind direction also tend to raise the sea level against the shore (in the northern hemisphere), owing to the effect of the earth's rotation. There are dynamic effects to be considered in both these cases as the wind is seldom so steady that static equilibrium is reached, except in small basins whose period of free oscillation is quite short.

The effect of the wind stress is enhanced by shoal water for the following reason, based on static considerations. Let us consider the balance of forces in one dimension only, say, the east-west direction. The stress caused by a west wind (blowing eastward) must be balanced by a slope of the sea surface in which its elevation increases eastward. The horizontal pressure gradient associated with this surface slope is essentially constant with depth, so that the greater the water depth the greater is the total force exerted on a vertical water column. Therefore a given surface slope will require greater wind stress to balance it in deeper water than in the shallower water.

Meteorologic disturbances over shallow seas have given rise to disastrous storm surges, such as those that frequently inundate the coasts of the North sea and the Gulf of Mexico. These surges frequently have a roughly periodic character with periods of the order of hours, and under severe conditions their amplitude can attain several metres. The horizontal stress on the water surface due to the wind is usually more important in these surges than the normal force due to the atmospheric pressure disturbance. Such variations of sea level cannot be predicted by the same procedures used to predict the astronomic tide, but considerable success has been obtained in understanding the dynamics of these phenomena, and in a few cases fairly accurate predictions have been made, particularly in the North sea area by a method developed by R. H. Corkan and Proudman. In order to make such a prediction the wind and pressure fields must be known (or estimated with sufficient accuracy) over the water surface of the region and for all necessary instants of time preceding the hour to be predicted.

Variations of water density, caused either by local heating and cooling or by advection of water of different properties, give rise to variations in elevation of the sea surface. If the change in surface level is calculated on the basis that the total water mass in a vertical column remains constant, the hydrostatic law shows that the relative height of the surface is

where a is the specific volume of the water, and P_b is the bottom pressure. The quantity , has been called the steric height, and is quite closely related to the dynamic height used in dynamical oceanography. Changes of the order of 10 cm. taking place from one month to the next are common in the ocean. In the seasonal variation of sea level the changes of density of the water are much more important than the long-period tidal constituents.