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, ATMACS gravity ,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.
- Deployment of window functions in combination with the Least Squares technology for improving analysis design and interpretation.