) 
The semi-monthly inequality 27 
2 The semi-monthly inequality 
The calculation of the tidal parameters is based on the analysis of the semi- 
monthly inequality (German: Halbmonatliche Ungleichheit, HU). Inequality is 
defined as the astronomically induced deviation of a tidal value (height or time) 
from the corresponding mean value. The semi-monthly inequality is caused by 
the fact that the positions of the Moon and Sun change periodically in relation to 
sach other. It is therefore the part of the total inequality that depends on the 
ohase of the Moon. 
In the area of the North Sea, the semi-monthly inequality is very clearly recog- 
nisable in the heights of the water levels. Figure 1 shows water level observa- 
tions from the tide gauge Cuxhaven, Steubenhöft. On the days after the new or 
full moon, higher high waters and lower low waters tend to occur (greater tidal 
range; spring time). On the days after the half moon, the high waters tend to be 
lower and the low waters higher (smaller tidal range; neap tide). Further infor- 
mation on spring and neap tides can be found, for example, in the publication 
‘Die Gezeiten - Entstehung und Phänomene” (Bundesamt für Seeschifffahrt 
und Hydrographie, 2022). 
In addition to the variation in height, periodic shifts also occur in the times of 
nigh and low waters. 
Cuxhaven 
rm 
5 
A 
E65 
zZ 
5x0 
K 
+ 
: 4.5 
4.0 
35 4 
" 
nd 
5 
1 
' 
m 
m: 
Cahum TUT 
Figure 1: Water level observations from the tide gauge Cuxhaven for April/May 2022. The water 
level height is relative to tide gauge zero (Pegelnullpunkt, PNP). Days with higher and lower tidal 
ranges alternate approximately every two weeks 
In the following, the period of the semi-monthly inequality, the connection to the 
transit times of the Moon, and the associated angular velocity are derived.