1. The functional model

1.1  Theoretical tides

1.1.1 Tide Generating Potential Development (TGP)

  • Providing a high-resolution structure for Tide Generating Potential (TGP) constituents
    • by identifying the main constituents of a wave group by their well-known Darwin symbols
    • by identifying constituents derived from the Moon’s ascending node and perigee as well from annual modulations and supplying them with new symbol names up to 10 character in lengths.
    • minor constituents with Darwin symbols are associated with a wave group and remain unchanged.
  • Implementation of this new structure for the TGPs of Hartmann, Wenzel 1995, Kudryavtsev 2003 and Tamura 1987.

1.1.2 Earth models

  • In addition to the WDZ Earth model, the  DDW-H and  DDW-NHi  Earth models are selectable for analysis.
  • Approximations of gravimetric and diminishing factors of potential degree 6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.
  • Approximations of Love and Shida numbers of potential degrees 4-6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.
  • Free core nutation modelling based on the supported Earth models for all tidal components including displacements and strains.
  • Alternatively using Earth model tidal parameters instead of adjusted parameters from a Least Squares analysis for calculating the observation residuals.

1.2  Optimal wave grouping

  • Generalizing the functional model by integrating constituents of degree 1 of the TGP.
  • Definition of reference potential functions Vij, i.e.
    • V20, V21, V22, V33, V44, V55, V66 
    • the Vij are totally covering the tidal frequency domains and each Vij only containing constituents j of a certain potential degree i.
  • Definition of non-reference or satellite potential functions Vkj of different potential degrees l than the reference potential functions  ( k .ne. i ) but possessing the same orders j  so that they share the same frequency domains  (e.g. V31 in V21, V32 in V22 etc.) :
    • V10, V11
    • V30, V31, V32
    • V40, V41, V42, V43
    • V50, V51, V52, V53, V54
    • V60, V61, V62, V63, V64, V65
  • Hypothesis free grouping of tidal constituents by means of reference and satellite wave groups defined by degree-dependent option codes.
  • Provision of templates for optimal wave grouping suited for different observation lengths like > 18 years, 4 years, 1 year.
  • Provision of the quality criterion “Correlation RMSE Amplifier (CRA)” for assessing the optimal wave group model.

1.3  Astronomical channels like pole and LOD tides

  • Pole and LOD tide information from
    • “IERS EOP PC Observatoire de Paris”, (http://hpiers.obspm.fr/eop-pc/index.php?index=C04& lang=en), or from
    • “The United States Naval Observatory (USNO) Washington”, ftp://maia.usno.navy.mil/ser7/finals2000A.all.
    • No extra programs are needed due to TAI-UT1 being tabulated or evaluated.
  • Interpolation of daily pole and LOD tide data to hourly and minute samples by cubic splines with continuous conditions or Lagrange interpolation.
  • Reduction of the astronomical channels from the tidal observations  by predefined reduction coefficients prior to a Least Squares analysis .

1.4  Meteorological regression channels

  • Modelling meteorological regression channels (e.g. station air pressure, ATMACS gravity ,etc.) by causal and/or  non – causal  impulse response functions of arbitrary lengths.
  • Estimating the associated frequency transfer functions yielding  frequency-dependent regression coefficients and phase shifts.
  • Reduction of the meteorological channels (e.g. station air pressure,  gravity due to attraction and loading of the atmosphere  etc.) from the tidal observations  by predefined reduction coefficients prior to a Least Squares analysis.

1.5  Polynomial model

  • Uniform polynomial model over the complete tidal record with identical coefficients for all blocks.

1.6  Non – linear and additional harmonics

  • Modelling of non-linear harmonics of tidal origin with known non-linear frequencies by an iterative feed-back analysis procedure.
  • Modelling of additional harmonics of tidal and/or non-tidal origin by an iterative feed-back analysis procedure.

1.7  Windows

  • Deployment of window functions in combination with the Least Squares technology for improving analysis design and interpretation.