Enhanced Earth and ocean tide analysis and prediction program system ETERNA-x

ETERNA-x is a program system for Earth and ocean tide parameter estimation and signal prediction. Compared to former Eterna 3.40, ETERNA-x reflects a lot of important enhancements in order to sophistically analyse and retrieve related information about the Earth concealed in tidal observations. The most important new features, released as system variant et34-x-v80-gnusim, are highlighted in the following:

  • 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 repositories of the Tide Generating Potential (TGP) developments of either
      • Hartmann-Wenzel (1995),
      • Kudryavtsev (2004),
      • Tamura (1987).
    • geodectic coefficients of all 3 TGPs enhanced by tidal potential degree 1 (V10, V11)
    • Earth models of
      • Dehant-Defraigne-Wahr Hydrostatic elastic (DDW-H),
      • Dehant-Defraigne-Wahr Non-Hydrostatic inelastic (DDW-NHi),
      • Wahr-Dehant-Zschau non-Hydrostatic inelastic (WDZ).
    • free core nutation (FCN) modelling and latitude dependent Love and Shida numbers also with Earth models DDW-H and DDW-NHi
    • hypothesis-free modelling of tidal wave groups belonging to potential functions of different degrees and orders but sharing the same frequency domains (e.g. V1, …, V6, V30,..,V32,..,V41,…,V43,…,V3:O1,…,V3:M2…)
    • astronomical channels (pole, LOD tide) daily sampled
      • interpolation of proper sampling by cubic splines with continuous conditions
      • Lagrange interpolation
    • enhanced modelling of meteorological regression channels 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,
    • repository as data description tool for modelling non-linear tidal constituents similar to the TGP
    • project dependent repositories as data description tools for modelling additional harmonics of unknown origin as well as their modulations,
    • overall Chebychev-polynomials for representing long periodic trends.
  • Enhanced Least squares (LS) parameter estimation
    • processing of data arbitrarily sampled from 1 min on
    • automated observation data sampling ( e.g. from 1 minute to 1 hour , 1 hour to 24 hours,… ) with alias filtering
    • providing alias FIR-filters
    • Earth tidal amplitude factors and phase leads including ocean load corrections
    • Static 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
    • parameter 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
    • consistent RMS error propagation of analysis parameters with correct handling of windows functions by the generalized error propagation law,
    • 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 reliably estimating the (residual) spectra of stochastic processes,
    • frequency dependent RMSE and confidence intervals of the parameters based on 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 up to the Nyquist frequency,
    • 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.
    • Tidal analysis and prediction implemented as 1 single program unit
  • 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 enhanced Eterna-x system variants.
  • Eterna-x systems on different computer and compiler platforms
    • Full GNU gfortran compatibility of the source code
    • Source code is supplied with all licences for free software
    • ————————————————————————————————–
    • operation system WINDOWS 10, always latest release
      • GNU gfortran representing standard Fortran 95
        • with SIMDEM/SIMFIT graphics support
          • Eterna system variant et34-x-v80-gnusim
    • operation system LINUX
      • GNU gfortran representing standard Fortran 95
        • does not support SIMDEM/SIMFIT graphics.
          • Eterna system variant et34-x-v74-lnxgnu

Keywords: ETERNA-x 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.