{"id":10113,"date":"2019-05-23T22:30:01","date_gmt":"2019-05-23T20:30:01","guid":{"rendered":"http:\/\/ggp.bkg.bund.de\/eterna\/?page_id=10113"},"modified":"2023-07-06T14:18:39","modified_gmt":"2023-07-06T12:18:39","slug":"earth-tide-analysis-and-prediction-program-system-et34-x-v73","status":"publish","type":"page","link":"\/eterna\/","title":{"rendered":"Enhanced Earth and ocean tide analysis and prediction program system ETERNA-x"},"content":{"rendered":"\r\n

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ETERNA-x is a program system for Earth and ocean tide parameter estimation and signal prediction. <\/span>Compared to former Eterna 3.40, ETERNA-x <\/span>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<\/span> in the following:<\/h4>\r\n\r\n\r\n\r\n\r\n\r\n
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  • The functional model of parameter estimation is represented by the Gauss-Markov model and subdued to the Least Squares (LS) principle including <\/strong>\r\n
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    • the tidal signal for gravity,tilt and all kinds of strains as well as enhanced static ocean tides<\/strong> based on the repositories of the Tide Generating Potential (TGP) developments of either\r\n
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      • Hartmann-Wenzel (1995),<\/li>\r\n
      • Kudryavtsev (2004),<\/li>\r\n
      • Tamura (1987).<\/li>\r\n<\/ul>\r\n<\/li>\r\n
      • geodectic coefficients of all 3 TGPs enhanced by tidal potential degree 1 (V10, V11)<\/strong><\/span><\/li>\r\n
      • Earth models of <\/strong><\/span>\r\n
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        • Dehant-Defraigne-Wahr Hydrostatic elastic (DDW-H),<\/strong><\/span><\/li>\r\n
        • Dehant-Defraigne-Wahr Non-Hydrostatic inelastic (DDW-NHi),<\/strong><\/span><\/li>\r\n
        • Wahr-Dehant-Zschau non-Hydrostatic inelastic (WDZ).<\/li>\r\n<\/ul>\r\n<\/li>\r\n
        • free core nutation (FCN) modelling and latitude dependent Love and Shida numbers also with Earth models DDW-H and DDW-NHi<\/strong><\/span><\/li>\r\n<\/ul>\r\n
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          • hypothesis-free modelling of tidal wave groups belonging to potential functions of different degrees and orders but sharing the same frequency domains<\/strong> (e.g. V1, …, V6, V30,..,V32,..,V41,…,V43,…,V3:O1,…,V3:M2…)<\/strong><\/span><\/li>\r\n
          • astronomical channels (pole, LOD tide) daily sampled<\/strong><\/span>\r\n
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            • interpolation of proper sampling by cubic splines with continuous conditions<\/strong><\/span><\/li>\r\n
            • Lagrange interpolation<\/li>\r\n<\/ul>\r\n<\/li>\r\n
            • enhanced modelling of meteorological regression channels with <\/strong><\/span>\r\n
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              • causal impulse response functions of arbitrary lengths,<\/strong><\/span><\/li>\r\n
              • non-causal impulse response functions of arbitrary lengths, <\/strong><\/span><\/li>\r\n
              • corresponding frequency transfer functions leading to frequency dependent regression coefficients and phase shifts, <\/strong><\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n
              • repository as data description tool for modelling non-linear tidal constituents similar to the TGP <\/strong><\/span><\/li>\r\n
              • project dependent repositories as data<\/span> description tools for modelling additional harmonics of unknown origin as well as their modulations,<\/span><\/span> <\/strong><\/li>\r\n
              • overall<\/strong><\/span> and block-wise Chebychev-polynomials for representing long periodic trends.<\/li>\r\n<\/ul>\r\n<\/li>\r\n
              • Enhanced Least squares (LS) parameter estimation <\/strong><\/span>\r\n
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                • processing of data arbitrarily sampled from 1 min on <\/strong><\/span><\/li>\r\n
                • automated observation data sampling ( e.g. from 1 minute to 1 hour , 1 hour to 24 hours,… ) with alias filtering <\/strong><\/span><\/li>\r\n
                • providing alias FIR-filters <\/strong><\/span><\/li>\r\n<\/ul>\r\n
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                  • Earth tidal amplitude factors and phase leads including ocean load corrections<\/strong><\/span><\/li>\r\n
                  • Static ocean tides:<\/span> amplitude factors and phase lags meeting oceanographic conventions<\/strong><\/span><\/span><\/li>\r\n
                  • non-linear tidal harmonic parameters<\/strong><\/span><\/li>\r\n
                  • harmonic parameters of additional non-tidal signals<\/strong><\/span><\/li>\r\n
                  • multi-channel impulse response functions leading to frequency transfer functions <\/strong><\/span><\/li>\r\n
                  • Overall<\/strong> and blockwise<\/span> <\/span>Chebychev polynomial coefficients of trend models<\/li>\r\n
                  • parameter estimation with different window functions\r\n
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                    • Rectangular window : highest possible frequency resolution (standard least squares),<\/li>\r\n
                    • Hanning window : best leakage properties,<\/li>\r\n<\/ul>\r\n<\/li>\r\n
                    • the \u201cSpectral Correlation Viewer (SCV)\u201d for illustrating the mutual algebraic correlations of the parameter estimates,<\/strong><\/span><\/li>\r\n
                    • the condition number an overall quality criterion of numerical stability.<\/li>\r\n<\/ul>\r\n<\/li>\r\n
                    • Enhanced stochastic model of the processes based on the Least Squares theory with <\/strong><\/span>\r\n
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                      • consistent RMS error propagation of analysis parameters with correct handling of windows functions by the generalized error propagation law, <\/strong><\/span><\/li>\r\n
                      • the \u201cCorrelation RMS Amplifier (CRA)\u201d indicating the increase of the \u201cRoot Mean Square Errors\u201d (RMSEs) of the parameters due to algebraic correlations, <\/strong><\/span><\/li>\r\n
                      • the autocovariance function (acf) of the residual process for <\/strong> reliably estimating the (residual) spectra of stochastic processes,<\/strong><\/span><\/li>\r\n
                      • frequency dependent RMSE and confidence intervals of the parameters based on the acf-based spectra , <\/strong><\/span><\/li>\r\n
                      • hypothesis tests on the goodness of statistical assumptions about probability distributions. <\/strong><\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n
                      • \u201cHigh Resolution Spectral Analyser (HRSA)\u201d for processing of LS residuals <\/strong><\/span>\r\n
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                        • spectral information on non-linear tidal signals up to the Nyquist frequency,<\/strong><\/span><\/li>\r\n<\/ul>\r\n
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                          • detecting additional spectral energies, <\/strong><\/span><\/li>\r\n
                          • iterative LS feed back procedure, <\/strong><\/span><\/li>\r\n
                          • whitening of the residual spectrum. <\/strong><\/span><\/li>\r\n<\/ul>\r\n<\/li>\r\n
                          • Comprehensive processing of load vectors and support of different ocean load phase models<\/strong><\/span>\r\n