Ocean Sci., 15, 1363-1379, 2019 
https://doi.org/10.5194/os-15-1363-2019 
© Author(s) 2019. This work is distributed under 
the Creative Commons Attribution 4.0 License. 
Ocean Science 
Reassessment of long-period constituents for tidal predictions along 
the German North Sea coast and its tidally influenced rivers 
Andreas Boesch and Sylvin Müller-Navarra 
Bundesamt flir Seeschifffahrt und Hydrographie, Bernhard-Nocht-Straße 78, 20359 Hamburg, Germany 
Correspondence: Andreas Boesch (andreas.boesch@bsh.de) 
- Published: 18 October 2019 
Received: 12 June 2019 - Discussion started: 18 June 2019 
Revised: 9 September 2019 - Accepted: 12 September 2019 
Abstract. The harmonic representation of inequalities 
(HRoI) is a procedure for tidal analysis and prediction that 
combines aspects of the non-harmonic and the harmonic 
method. With this technique, the deviations of heights and 
lunitidal intervals, especially of high and low waters, from 
their respective mean values are represented by superpo 
sitions of long-period tidal constituents. This article docu 
ments the preparation of a constituents list for the opera 
tional application of the harmonic representation of inequal 
ities. Frequency analyses of observed heights and lunitidal 
intervals of high and low water from 111 tide gauges along 
the German North Sea coast and its tidally influenced rivers 
have been carried out using the generalized Lomb-Scargle 
periodogram. One comprehensive list of partial tides is re 
alized by combining the separate frequency analyses and by 
applying subsequent improvements, e.g. through manual in 
spections of long time series data. The new set of 39 partial 
tides largely confirms the previously used set with 43 par 
tial tides. Nine constituents are added and 13 partial tides, 
mostly in the close neighbourhood of strong spectral com 
ponents, are removed. The effect of these changes has been 
studied by comparing predictions with observations from 98 
tide gauges. Using the new set of constituents, the standard 
deviations of the residuals are reduced on average by 2.41 % 
(times) and 2.30 % (heights) for the year 2016. The new set 
of constituents will be used for tidal analyses and predictions 
starting with the German tide tables for the year 2020. 
1 Introduction 
Tidal predictions for the German Bight are calculated at the 
Federal Maritime and Hydrographic Agency (Bundesamt für 
Seeschifffahrt und Hydrographie, BSH) and are published in 
official tide tables each year. The preparation of tidal predic 
tions has a long tradition at BSH and its predecessor institu 
tions: the first tide tables by the German Imperial Admiralty 
were issued for the year 1879. 
Since 1954, a method named harmonic representation of 
inequalities (HRoI) has been used at BSH to calculate tidal 
predictions for tide gauge locations along the German North 
Sea coast and its tidally influenced rivers (Horn, 1948, 1960; 
Müller-Navarra, 2013). This technique allows for analysing 
the deviations of times and heights, especially at high and 
low water, from their respective mean values. In contrast to 
the widely used harmonic method (e.g. Parker, 2007, and ref 
erences therein), the HRoI utilizes only long-period partial 
tides. This reduction in frequency space allows for a compu 
tationally efficient way to calculate times and heights of high 
and low water. Other techniques for tidal analysis of high and 
low waters have been described in Doodson (1951) and Fore 
man and Henry (1979); these two methods additionally con 
sider diurnal and semi-diurnal constituents. The HRoI has 
proven to be especially useful for predicting semi-diurnal 
tides in shallow waters where the harmonic method would 
need a large number (>60) of constituents or could even fail 
to produce adequate results. The fundamentals of the HRoI 
are summarized in Sect. 2 for completeness. 
An important aspect of tidal prediction is the selection of 
relevant partial tides (angular velocities, w) to be included 
in the underlying analysis of water level records. While it is 
possible to determine these partial tides individually for each 
single tidal analysis, it is desirable in an operational service 
Published by Copernicus Publications on behalf of the European Geosciences Union.