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.