It is now of interest to inquire into the matter of how much the mean sea level at a given latitude would be effected by a relatively small alteration in the speed of the earth's rotation. In the development of Eq. (88) we have seen that only half of the magnitude of can be attributed directly to the effect of the earth's rotation. Half of the effect is due to the variation of with latitude associated with the distorted shape of the lithosphere, and thus indirectly related to the centrifugal force of the earth's rotation.
In attempting to predict how much the sea level will be altered with a given change in , the question arises as to whether or not the earth's solid mantle will be altered as well and, if so, by how much? An alteration of the shape of the earth's mantle would have a two-fold effect: (1) the redistribution of mass would alter the latitudinal variation of and thus influence the shape of the sea level in addition to the direct effect of the altered centrifugal force on the water; and (2) the change is shape of the solid crust will tend to reduce the apparent change in water lwvel which can only be measured relative to the earth's crust. It is conceivable that for the very slow secular reductino of which results from the frictional influences of the earth and sea tides the mantle is altered in about the same manner as the sea surface. However, for the relatively rapid variations of which are known to occur during the year and even over periods of a few weeks ( (), Munk and Miller (1950), Lawford and Veley (1951)), it would seem reasonable to expect that the earth's crust cannot respond commensurate with the varying centrifugal force, and that only the sea itself will be fully responsive.
For the latter situation, if we assume no change in the mantle then the distribution of should remain essentially unaltered except for the second order effect due to the altered distribution of the mass of the sea itself. Consequently, we must regard Eq. (88) as of the the form
where meters is invariant. It can then be shown that
where T is the period of rotation of the earth about its axis. On the basis of Eq. (90) and Table 2.07-I we see that the increase of at the equator corresponding to a decrease of the length of the day of one second is
The corresponding drop of sea level at the North pole would be 16.6 cm (or about 6.5 inches). At latitude 35.1 N or S the sea level would be unaffected.
The variations in the length of the day are actually of the order of milliseconds and the associated changes in sea level are therefore only fractions of a millimeter. However, the important aspect of the above considerations with respect to the earth is the effect of the alterations in the position and magnitude of the solar tidal bulge during the course of a year. The varying declination of the sun induces a slight shift in the mass of water above or below the equatoar which, in turn, alters the length of the day (Mintz and Munk (1951), Munk and Revelle (1952)). This effect must therefore be taken into account when interpreting observations of the changes in the length of the day before drawing any conclusions as regards changes in the atmospheric circulation.