3. Least Squares parameter estimation based on the Gauss-Markov-model

3.1     Parameter estimation

  • Maximum resolution LS estimators for all parameters of the functional model.
  • Minimum leakage LS estimators for all parameters of the functional model.
  • Estimation of tidal parameters of different potential degrees and orders.
  • Estimation of tidal parameters meeting oceanographic definitions and conventions
  • Correlation analysis of selected parameters by the “SPECTRAL CORRELATION VIEWER (SCV)” with graphic support.
  • Calculation of the “Correlation RMSE Amplifier (CRA)” of each tidal and non-tidal wave group.
  • Assessment of optimal wave grouping by means of the CRAs.
  • Iterative analysis procedure to “whiten” the residuals.

3.2     Reduction mode processing by means of PASSGROUPS and STOPGROUPS

  • Reduction of the observations by channels with predefined reduction factors prior to analysis.
  • Pre-processing analysis of tidal observations to yield reduced observations containing unmodelled signals, noise and a groups of signals defined as Pass Groups ( example: only the long periodic signals for subsequent analysis).  The resulting  data file  is of type *.pas in the ETERNA data format.
  • Pre-processing analysis of tidal observations to subtract a defined  group of signals, the Stop Groups (example: signals beyond a certain frequency to avoid aliasing when increasing the sampling interval). The resulting  data file  is of type *.stp in the ETERNA data format.

3.3     “High Resolution Spectral Analyser (HRSA)”

  • Domain-wise analysing the residuals.
  • Estimating and presenting residual spectra together with their signal to noise ratios to detect hidden signals.
  • Deriving spectral information for frequency-dependent RMSEs and confidence intervals.

3.4     Residual vector information

  • Calculation of residual vectors B (B, beta) for all modelled main Earth tide constituents as difference of the (observed=analysed) tidal parameters and those derived from the chosen Earth model.
  • Calculation of mean load vectors L (L, lambda)  based on different ocean models and processing Greenwich and local tidal phase lags/leads.
  • Calculation of ocean load corrected amplitude factors and phase shifts for the main tidal constituents.
  • Calculation of residual vectors x (x, chi) based on the ocean load corrected observed tidal parameters and those of  the provided Earth models for the main tidal wave groups.
  • Consistency check by comparing the load vectors L from ocean models with the residual vectors B of the analysis.
  • Comparing the ocean corrected amplitude factors with those of the Earth models implemented.

3.5     Miscellaneous Information enhancements

  • Thorough parameterization (*.ini) for gaining utmost flexibility for Earth tide analysis and prediction.
  • Comprehensive consistency checks on syntax, domains, and inter parameter rules for the parameters in *.ini.
  • Analysing regression channels with the functional model of Earth tides prior to Earth tide analysis.
  • Enhanced block/gap management (minimum block lengths, automated elimination of blocks).
  • Providing online graphic presentation support for a better interpretation of the analysis results by the open source SIMDEM/SIMFIT package.
  • Flexible output parameters to control the flow of information.
  • Support of nano radiant dimension for tilt.