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  superpositions ­
  of  long-period  tidal  constituents.  This  article  documents ­
  the  preparation  of  a  constituents  list  for  the  operational ­
  application  of  the  harmonic  representation  of  inequalities. ­
  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  realized ­
  by  combining  the  separate  frequency  analyses  and  by
applying  subsequent  improvements,  e.g.  through  manual  inspections ­
  of  long  time  series  data.  The  new  set  of  39  partial
tides  largely  confirms  the  previously  used  set  with  43  partial ­
  tides.  Nine  constituents  are  added  and  13  partial  tides,
mostly  in  the  close  neighbourhood  of  strong  spectral  components, ­
  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  predictions ­
  has  a  long  tradition  at  BSH  and  its  predecessor  institutions: ­
  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  references ­
  therein),  the  HRoI  utilizes  only  long-period  partial
tides.  This  reduction  in  frequency  space  allows  for  a  computationally ­
  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  Foreman ­
  and  Henry  (1979);  these  two  methods  additionally  consider ­
  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.