Arithmetical  Operation

17

c)  Processing  of  19  years  of  gauge  observations
The  astronomical  rudiments  of  tidal  theory  have  been  sufficiently  described
(Horn,  1948).  From  these  derives,  amongst  other  things,  the  demand  for  the
simultaneous  analysis  of  respective  time  periods  of  at  least  19  years.  Table  6  in
the  appendix  shows  the  beginning  (31  Dec  1990,  23:45  UTC)  and  the  end
(31  Dec  2009,  18:15  UTC)  of  the  time  period  of  vertex  observations  at  the  Cuxhaven ­
  gauging  station,  transit  times  of  the  Moon  and  syntheses.
The  observed  vertex  times  and  levels  (Table  6,  Columns  5  and  7)  must  first  be
paired  with  the  Moon  transits  (Columns  1  and  2).  For  this,  definite  mapping  can
be  achieved  for  calm  weather  conditions  (Müller-Navarra,  2009).  In  the  event  of
strong  storms,  when  onset  times  deviate  from  HWT  and  LWT  by  several  hours,
amends  are  required.  Yet  this,  too,  may  be  largely  automated.  The  data  set  from
the  Cuxhaven  gauging  station  -  the  basis  for  these  analyses  -  ranges  from
high  water  after  lower  culmination  (1=14467,  k=3)  to  low  water  after  upper  culmination ­
  (1=21172,  k=2).
In  the  case  of  the  hydrograph  Illustration,  for  the  same  period  of  time,  each
transit  at  upper  culmination  Is  assigned  96  subsequent  sampling  points  (see
above).
d)  Filtering  of  data
Since  the  water  level  measured  at  coastal  gauging  stations  proves  to  be  very
susceptible  to  wind,  cumulative  stormy  years  with  many  storm  surges  or  long
periods  of  lowered  water  levels  can  “spoil”  the  forecast,  especially  as  regards
the  long-periodic  elements.  Filtering  of  the  19-year  time  series  has  proven  itself
in  practice,  excluding  all  individual  cases  deviating  by  more  than  3  standard
deviations  from  the  mean  value.  Table  3  shows  mean  values  and  standard  deviations ­
  for  the  observation,  the  filtered  data  set  and  the  vertex  value  forecast.  Filtering ­
  cancels  out  only  0.1  %  of  data  as  regards  the  onset  times  and  approximately ­
  1.5%  of  observations  as  regards  the  water  levels.
In  the  case  of  hydrograph  processing,  the  mean  values  and  the  standard  deviation ­
  (SD)  are  represented  in  a  graph  (Figure  1).  Here,  the  numbers  of  cases  m
average  at  6623  and,  after  filtering,  at  6563  of  6689  possible  numbers.  It  is  conspicuous ­
  that  the  greatest  standard  deviations  occur  approximately  2  h  after
LWT.  This  Is  precisely  where  the  main  problem  of  hydrograph  forecasting  for
tidal  rivers  lies.  The  further  upstream  the  tide  gauge,  the  shorter  the  flood  duration ­
  and  the  faster  the  water  level  rises.  In  extreme  cases,  sometimes  also  only
at  spring  tide,  this  can  result  in  phenomena  akin  to  tidal  bores  with  flood  durations ­
  being  virtually  zero.