252 Principal Features of Tidal Phenomena 



ocean from atmospheric pressure observations made on board of a ship; he 

 has shown how to compute the M 2 component from hourly or 4-hourly ship 

 observations. First, one has to determine the daily pressure curve with 

 a period of a solar day. These values are then subtracted from the hourly 

 observations and the residual values are analysed for a 25 h lunar wave. 

 The lunar pressure wave obtained in this manner is composed of three parts. 



(1) Of the atmospheric tide {d x p), which is known with sufficient accuracy 

 from the results of the atmospheric pressure analysis made at land stations 

 and can, therefore, be eliminated. 



(2) Of the oscillations of the air-masses generated by the ocean tides, which 

 cause the rise and fall of the isobaric surfaces (d 2 p). This influence of the ocean 

 waves (also of tides) on the atmosphere, which was formerly disregarded, has 

 been given by Chapman (1919, p. 128) for plane waves in an atmosphere 

 with a uniform vertical temperature gradient. It appears that, for very slow 

 waves (velocity of propagation c < c , the velocity of propagation of free 

 waves in the atmosphere) the disturbances in the atmosphere caused by the 

 ocean waves become negligible, i.e. the isobaric surfaces remain undisturbed. 

 On the contrary, for fast waves (c > c ) the atmosphere participates in the 

 wave motion of the water, the isobaric surfaces rise and fall parallel to the 

 sea surface. Generally and in most cases, c < c . Then the phase of the 

 atmospheric wave is opposed to the phase of the water waves, i.e. the isobaric 

 surfaces lie lower above the crest than above the trough of the wave. 



(3) The third part is the variation in pressure (d 3 p) caused by the rise 

 and fall of the ship by the tide, according to the barometric altitude formula. 



If d x p is eliminated, then only the action of the motion of the sea surface 

 remains in the observed variation. This action is expressed by Bartels in the 

 following relation: 



Ap = d 2 p+d 3 p = xd 3 p , 

 in which 



1 



x ~\-(c/c y 



From the distribution of the co-tidal lines (see charts I and II) one can 

 derive, for instance, the velocity of propagation of the tidal waves in the 

 South Atlantic c = 1-80 x 10 4 cm/sec, whereas with convective equilibrium in 

 the atmosphere one obtains c = 2-94 x 10 4 cm/sec. Then c : c = 0-61 ; the 

 increasing factor becomes x = 1-6, with c = 10 4 cm/sec (about 1000 m depth) 

 it becomes 113, with c = 6-3 x 10 4 cm/sec (depth 400 m) 105. Hence, the 

 co-oscillation of the atmosphere with the ocean tides is very important and 

 should be considered in order to obtain a correct value for d 3 p. From these 

 corrected values the amplitude and the phase of the M 2 tide can then 

 easily be derived. 



