A. Boesch and S. Müller-Navarra: Reassessment of long-period constituents for tidal predictions 
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Ocean Sei., 15,1363-1379, 2019 
The parameters ajJ — 0 2L are determined from a 
least-squares fit, i.e. 
J 
x 2 = X (yj ~ yj) 2 min ' (2) 
7=0 
where yj is the observed heights or lunitidal intervals. The 
angular velocities o>¡ (° tn -1 ) are taken from a previously de 
fined set of L partial tides. In Table 2, we list two sets of 
partial tides that have been used in the past at BSH and the 
new set that is the result of this work. 
All tidal constituents considered here have angular veloci 
ties that are linear combinations of the rate of change of four 
fundamental astronomical arguments: the mean longitude 
of the moon (v), the mean longitude of the sun (h), the 
mean longitude of the lunar perigee (p) and the negative 
of the longitude of the moon’s ascending node (N'). The 
second to fifth columns in Table 2 give the respective linear 
coefficients m. The two other arguments that one encounters 
using the harmonic method can be effectively neglected: 
the coefficients for the rate of change of the mean lunar 
time and of the mean longitude of the solar perigee are 
always equal to zero because only long-period constituents 
need to be considered and the time series are too short to 
resolve differences due to the variations in the solar perigee. 
The angular velocities in the sixth and seventh columns 
are given in degrees per hour and in degrees per transit 
number (tn), respectively. The conversion between these two 
units is 1° tn -1 •rfjj] = 1° h -1 with the length of the mean 
lunar day r = 24.84120312 htn -1 . The angular velocities 
are calculated using the expressions for the fundamental 
astronomical arguments as published by the International 
Earth Rotation and Reference Systems Service (2010, 
Sect. 5.7). The alphabetical Doodson number is given in 
the first column (Doodson, 1921; Simon, 2013). The eighth 
column states the commonly used names (e.g. see the Inter 
national Hydrographic Organization (IHO) Standard List of 
Tidal Constituents: https://www.iho.int/mtg_docs/com_wg/ 
IHOTC/IHOTC_Misc/TWCWG_Consti tuent_list.pdf, last 
access: 4 October 2019). An “x” mark in one of the last three 
columns indicates whether the angular velocity is included 
in the respective constituents list for usage with the HRoI. 
3 Tide gauge data 
The tide gauges at the German coast and in rivers are oper 
ated by different federal and state authorities. These agen 
cies provide BSH with quality-checked water level records 
of high and low waters (times and heights). Table A1 in the 
Appendix lists 137 German tide gauges which deliver water 
level observations on a regular basis and for which tidal pre 
dictions were published in BSH tide tables (Gezeitentafeln) 
or the tide calendar (Gezeitenkalender) for the year 2018 
(Bundesamt flir Seeschifffahrt und Hydrographie, 2017a, b). 
Figure 1. The locations of all tide gauges in the German Bight from 
Table Al. Some of the tide gauges mentioned in the text are high 
lighted: Borkum, Fischerbalje (B ); Emden, Große Seeschleuse (E); 
Cuxhaven, Steubenhöft (C); and Hamburg, St. Pauli (H). 
For the analysis presented in Sect. 4, all data until the year 
2015 that were systematically archived in electronic form 
at the BSH tidal information service are considered (as of 
August 2018). The data periods are given in the fourth and 
fifth columns in Table Al and cover 22-27 years for most 
gauges. Much longer time series were readily available for 
tide gauges at Cuxhaven (BSH gauge number 506P) and 
Hamburg (508P) for which data since the year 1901 are used. 
We are aware that the tidal regime can change over such a 
long time but include all available data in the analysis to max 
imize the achievable spectral resolution. 
Only tide gauges with more than 19 years of data are in 
cluded in order to cover the period of rotation of the lunar 
node (18.6 years) in the frequency analysis. In addition, we 
use only tide gauges where more than 60 % of high and low 
waters are recorded during the gauge’s data period. This cri 
terion excludes gauges for which no low-water observations 
are available. The 111 gauges that fulfil these two criteria 
are marked in the column labelled “Used for analysis’’ in Ta 
ble Al. The locations of all tide gauges are shown on the map 
in Fig. 1. 
4 Analysis of high-water and low-water time series 
The following analysis is applied to the water level records 
of all 111 tide gauges that are marked in the seventh column 
of Table Al in the Appendix.