Enhanced Earth and ocean tides analysis and prediction program system ETERNA et34-x-v74-*

ETERNA et34-x-v74-* is a program system for Earth and ocean tides parameter estimation and signal prediction. It is based on the Eterna 3.40 version but enhanced by a lot of important features highlighted:

  • The functional model of parameter estimation is represented by the Gauss-Markov model and subdued to the Least Squares (LS) principle including
    • the tidal signal for gravity,tilt and all kinds of strains as well as enhanced static ocean tides based on the Tide Generating Potential (TGP) developments of either
      • Hartmann-Wenzel (1995),
      • Kudryavtsev (2004),
      • Tamura (1987).
    • All TGPs enhanced by the tidal potential degree 1 (V10, V11)
    • Earth models of
      • Dehant-Defraigne-Wahr Hydrostatic elastic (DDH),
      • Dehant-Defraigne-Wahr non-Hydrostatic inelastic (DDNHi),
      • Wahr-Dehant-Zschau non-Hydrostatic inelastic (WDZ).
    • free core nutation (FCN) modelling and latitude dependent Love and Shida numbers,
    • a hypothesis-free modelling of wave groups belonging to potential functions of different degrees and orders but sharing the same frequency domains,
    • enhanced modelling of physical (meteorological, astronomical) regression processes with
      • causal impulse response functions of arbitrary lengths,
      • non-causal impulse response functions of arbitrary lengths,
      • corresponding frequency transfer functions leading to frequency dependent regression coefficients and phase shifts,
    • additional harmonics of unknown origin as well as its modulations,
    • Overall Chebychev-polynomials for representing long periodic trends.
  • Enhanced Least squares (LS) parameter estimation
    • Flexible observation data sampling (minute to hour etc)
    • Earth tidal amplitude factors and phase leads
    • Ocean tides amplitude factors and phase lags meeting oceanographic conventions
    • non-linear tidal harmonic parameters
    • harmonic parameters of additional non-tidal signals
    • multi-channel impulse response functions leading to frequency transfer functions
    • Overall Chebychev polynomial coefficients of trend models
    • estimation with different window functions
      • Rectangular window : highest possible frequency resolution (standard least squares),
      • Hanning window : best leakage properties,
    • the “Spectral Correlation Viewer (SCV)” for illustrating the mutual algebraic correlations of the parameter estimates,
    • the condition number an overall quality criterion of numerical stability.
  • Enhanced stochastic model of the processes based on the Least Squares theory with
    • the “Correlation RMS Amplifier (CRA)” indicating the increase of the “Root Mean Square Errors” (RMSEs) of the parameters due to algebraic correlations,
    • the autocovariance function (acf) of the residual process for estimating reliable residual spectra,
    • frequency dependent RMSE and confidence intervals of the parameters from the acf-based spectra ,
    • hypothesis tests on the goodness of statistical assumptions about probability distributions.
  • “High Resolution Spectral Analyser (HRSA)” for processing of LS residuals
    • spectral information on non-linear tidal signals ,
    • detecting additional spectral energies,
    • iterative LS feed back procedure,
    • whitening of the residual spectrum.
  • Comprehensive processing of load vectors and support of different ocean load phase models
    • ocean load corrected Earth tide parameter estimates,
    • residuals vectors for detecting the impact of additional signals in the tidal frequency bands.
    • residual vectors of meterorological channels for detecting its impact on the tidal parameters
  • Comprehensive Earth tide signal prediction including ocean load vectors
    • based on one of the 3 Earth models ,
    • based on the ocean load vector information
    • based on tidal analysis parameters of prior analyses including the enhanced TGPs.
  • Comprehensive graphic support for assessment
    • time series like windows, observations, residuals, auto cov. fct., statistical distribution fcts.
    • spectra like FIR transfer fcts, windows, SCV, residual spectra, HRSA-spectra, freq. transfer fcts. of regression channels
  • Comprehensive documentation for all aspects of the program
    • Manual-01: Theory ,
    • Manual-02: Users Guide,
    • Manual-03: Installation Guides for all Eterna system variants.
  • Eterna systems on different computer and compiler platforms
    • operation system WINDOWS 10, latest release
      • Silverfrost Fortran FTN95
        • with SIMDEM/SIMFIT graphics support
          • Eterna system variant et34-x-v74-winsil
      • GNU gfortran representing standard Fortran 95
        • does not support SIMDEM/SIMFIT graphics,
          • Eterna system variant et34-x-v74-wingnu
    • operation system LINUX
      • GNU gfortran representing standard Fortran 95
        • does not support SIMDEM/SIMFIT graphics.
          • Eterna system variant et34-x-v74-lnxgnu

Keywords: ETERNA enhancements, Earth tides, ocean tides, pole tides, LOD tides, TGP, V1, Earth models, FCN, Earth tide observations, tide gauge observations, meteorological channels, FIR-filters, Gauss-Markov model, Least Squares (LS), parameter estimation, window functions, reduction models, tidal parameters, regression analysis, impulse response functions, frequency transfer functions, Correlation Viewer(SCV), correlation RMS amplifier (CRA), LS error propagation, Root Mean Square Error (RMSE), probability distribution, probability density, goodness hypothesis tests, confidence intervals, autocovariance function, spectral analysis, power spectrum, High Resolution Spectral Analyser (HRSA), Earth tide signal prediction.