30 | Berichte des BSH Nr. 57 
DU 
Modelling the water level data and calculating the tidal 
parameters 
3.1 
Modelling 
with sufficient 
observation 
data 
The input data for calculating the tidal parameters are measured heights and 
times of high and low waters®. The times are converted into intervals, i.e. the time 
difference between the occurrence of the high or low water and the associated 
preceding lunar transit. Both times must be expressed in the same time zone. As 
a rule, the lunar transit at the prime meridian and all times in UTC are used. 
The observation data is modelled using truncated Fourier series. These include 
the fundamental oscillation of the half synodic month and three harmonics. 
The heights and intervals of the high and low waters are assigned to the transit 
limes of the moon and are expressed as a function of these transit times. 
This results in the following four systems of equations for the high and low water 
heights (HWH, NH) and the high and low water intervals (HWI, NW): 
4 
Yuwu (€) = Aywao + )aC cos(iot) + bywu.isin(iot)) 
—_ 
4 
Yawa (6) = ) i 
Nwa(t) = Aywao * DD anwe cos(iot) + bywu.isin(iot)) 
i=1 ; 
Yuwı (©) = Aywıo + 
4 
CH cos(igt) + bywi.:sin(iot)) 
i=1 
4 
Yawı(E) = Aywıo + Dan cos(iogt) + bywi:sin(iot)) 
i1—1 
Here, y is the observed altitude (in metres) or the observed tidal interval (in 
nours), co’ is the angular velocity of the semi-monthly inequality (30°/Trh) and fis 
the time of the lunar transit assigned to the height or interval (hours since mid- 
night or noon). The range of values is t= [0,12). 
The Fourier series is cancelled after the fourth element in order to reduce the 
influence of non-astronomical effects in the analysis. The introduction of further 
alements does not bring any significant improvements. The third harmonic (/=4) 
represents one eighth ofthe synodic month (period approx. 3.69 days) and 
corresponds to the partial tide with the lowest frequency for the tidal analysis 
with the harmonic representation of the inequalities according to the operational 
partial tide list (Boesch & Müller-Navarra, 2019). 
The coefficients ag, a; and b; are calculated using the least squares method 
(e.g. Press et al., 1992). The calculated coefficients can be used to calculate 
the tidal parameters (see Section 3.3). 
3 Calculated/simulated heiahts and times can also be used instead of observed water levels