On the Variation of Sea Level Caused by the Variation of Atmospheric Pressure

An Investigation on Meteorological Tides in the Neighbouring Seas of Japan-First paper

Abstract

The height of the sea level changes as the atmospheric pressure varies. Their phases, however, do not always coincide, but generally the level change lags behind the pressure change by a few hours. Moreover, Dr. S. Ogura found that this time retardation seems to increase with latitude in the neighbouring seas of Japan.
As the result of investigation of the velocity distribution with depth in case of tidal currents and high tides caused by surface pressure and of the decay of long waves sent out from a wave source, the present author showed that we may consider a resistance proportional to the velocity of fluid particle in place of eddy viscosity as a frictional force acting on a long wave. Using this particular form of resistance and assuming that the motion is simple harmonic, the equation to be solved is where ζ^* is the equilibrium elevation, h is the depth of sea and k, λ are the coefficient of resistance and that of Coriolis' force respectively. By solving this equation, we have the phase difference ε between surface pressure and the corresponding change of sea level, that is approximately, where T and U are the period and velocity of surface pressure respectively.
Since the result of calculation by the above formula essentially agrees with that of observations, we may conclude that the said phase retardation is due to the resistance acting on sea water. Moreover, we can explain the reason why the time retardation increases with latitude by considering the depth of sea, velocity and period of surface pressure and Coriolis' force.
Though in the above discussion we have assumed a simple harmonic variation of surface pressure, it can be shown that the conclusions above obtained are also valid in case of a solitary wave of surface pressure by using Fourier's integrals. And the author showed a method to discuss the level change in case of an arbitrary type of change of surface pressure by using Fourier's transformation. In case of a finitely extended ocean, the phase retardation is larger or smaller by ten to twenty percent than in case of an infinitely extended ocean according to the relations between geographical features and the direction of propagation of surface pressure. Thus, it was found that the effect of land is small in our present problem.