{"id":6073,"date":"2018-06-05T20:39:08","date_gmt":"2018-06-05T18:39:08","guid":{"rendered":"http:\/\/ggp.bkg.bund.de\/eterna\/?page_id=6073"},"modified":"2023-07-06T14:18:39","modified_gmt":"2023-07-06T12:18:39","slug":"functional-model","status":"publish","type":"page","link":"\/eterna\/?page_id=6073","title":{"rendered":"1.  The functional model"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#11_Theoretical_tides\">1.1\u00a0 Theoretical tides<\/a><ul><li><ul><li><a href=\"#111_Tide_Generating_Potential_Development_TGP\">1.1.1 Tide Generating Potential Development (TGP)<\/a><\/li><li><a href=\"#112_Earth_models\">1.1.2 Earth models<\/a><\/li><\/ul><\/li><li><a href=\"#12_Optimal_wave_grouping\">1.2\u00a0 Optimal wave grouping<\/a><\/li><li><a href=\"#13_Astronomical_channels_like_pole_and_LOD_tides\">1.3\u00a0 Astronomical channels like pole and LOD tides<\/a><\/li><li><a href=\"#14_Meteorological_regression_channels\">1.4\u00a0 Meteorological regression channels<\/a><\/li><li><a href=\"#15_Polynomial_model\">1.5\u00a0 Polynomial model<\/a><\/li><li><a href=\"#16_Non_8211_linear_and_additional_harmonics\">1.6\u00a0 Non &#8211; linear and additional harmonics<\/a><\/li><li><a href=\"#17_Windows\">1.7\u00a0 Windows<\/a><\/li><\/ul><\/li><\/ul><\/div>\n<h2><span id=\"11_Theoretical_tides\">1.1\u00a0 Theoretical tides<\/span><\/h2>\n<h4><span id=\"111_Tide_Generating_Potential_Development_TGP\">1.1.1 Tide Generating Potential Development (TGP)<\/span><\/h4>\n<ul>\n<li>Providing a high-resolution structure for Tide Generating Potential (TGP) constituents\n<ul>\n<li>by identifying the main constituents of a wave group by their well-known Darwin symbols<\/li>\n<li>by identifying constituents derived from the Moon\u2019s ascending node and perigee as well from annual modulations and supplying them with new symbol names up to 10 character in lengths.<\/li>\n<li>minor constituents with Darwin symbols are associated with a wave group and remain unchanged.<\/li>\n<\/ul>\n<\/li>\n<li>Implementation of this new structure for the TGPs of Hartmann, Wenzel 1995, Kudryavtsev 2003 and Tamura 1987.<\/li>\n<\/ul>\n<h4><span id=\"112_Earth_models\">1.1.2 Earth models<\/span><\/h4>\n<ul>\n<li>In addition to the WDZ Earth model, the \u00a0DDW-H and \u00a0DDW-NHi \u00a0Earth models are selectable for analysis.<\/li>\n<li>Approximations of gravimetric and diminishing factors of potential degree 6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.<\/li>\n<li>Approximations of Love and Shida numbers of potential degrees 4-6 for all supported Earth models based on the Gutenberg-Bullen-A Earth model.<\/li>\n<li>Free core nutation modelling based on the supported Earth models for all tidal components including displacements and strains.<\/li>\n<li>Alternatively using Earth model tidal parameters instead of adjusted parameters from a Least Squares analysis for calculating the observation residuals.<\/li>\n<\/ul>\n<h3><span id=\"12_Optimal_wave_grouping\">1.2\u00a0 Optimal wave grouping<\/span><\/h3>\n<ul>\n<li>Generalizing the functional model by integrating constituents of degree 1 of the TGP.<\/li>\n<li>Definition of reference potential functions Vij, i.e.\n<ul>\n<li><strong>V20, V21, V22, V33, V44, V55, V66\u00a0<\/strong><\/li>\n<li>the Vij are totally covering the tidal frequency domains and each Vij only containing constituents j of a certain potential degree i.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li>Definition of non-reference or satellite potential functions Vkj of different potential degrees l than the reference potential functions\u00a0 ( k .ne. i ) but possessing the same orders j \u00a0so that they share the same frequency domains \u00a0(e.g. V31 in V21, V32 in V22 etc.) :\n<ul>\n<li><strong>V10, V11<\/strong><\/li>\n<li><strong>V30, V31, V32<\/strong><\/li>\n<li><strong>V40, V41, V42, V43<\/strong><\/li>\n<li><strong>V50, V51, V52, V53, V54<\/strong><\/li>\n<li><strong>V60, V61, V62, V63, V64, V65<\/strong><\/li>\n<\/ul>\n<\/li>\n<li>Hypothesis free grouping of tidal constituents by means of reference and satellite wave groups defined by degree-dependent option codes.<\/li>\n<li>Provision of templates for optimal wave grouping suited for different observation lengths like &gt; 18 years, 4 years, 1 year.<\/li>\n<li>Provision of the quality criterion \u201cCorrelation RMSE Amplifier (CRA)\u201d for assessing the optimal wave group model.<\/li>\n<\/ul>\n<h3><span id=\"13_Astronomical_channels_like_pole_and_LOD_tides\">1.3\u00a0 Astronomical channels like pole and LOD tides<\/span><\/h3>\n<ul>\n<li>Pole and LOD tide information from\n<ul>\n<li><strong>&#8220;IERS EOP PC Observatoire de Paris&#8221;, (http:\/\/hpiers.obspm.fr\/eop-pc\/index.php?index=C04&amp; lang=en)<\/strong>, or from<\/li>\n<li><strong>&#8220;The United States Naval Observatory (USNO) Washington&#8221;, ftp:\/\/maia.usno.navy.mil\/ser7\/finals2000A.all<\/strong>.<\/li>\n<li>No extra programs are needed due to TAI-UT1 being tabulated or evaluated.<\/li>\n<\/ul>\n<\/li>\n<li>Interpolation of daily pole and LOD tide data to hourly and minute samples by cubic splines with continuous conditions or Lagrange interpolation.<\/li>\n<li>Reduction of the astronomical channels from the tidal observations\u00a0 by predefined reduction coefficients prior to a Least Squares analysis .<\/li>\n<\/ul>\n<h3><span id=\"14_Meteorological_regression_channels\">1.4\u00a0 Meteorological regression channels<\/span><\/h3>\n<ul>\n<li>Modelling meteorological regression channels (e.g. station air pressure, ATMACS gravity ,etc.) by <strong>causal and\/or\u00a0 non &#8211; causal\u00a0 impulse response functions of arbitrary lengths<\/strong>.<\/li>\n<li>Estimating the associated frequency transfer functions yielding\u00a0 frequency-dependent regression coefficients and phase shifts.<\/li>\n<li>Reduction of the meteorological channels (e.g. station air pressure,\u00a0 gravity due to attraction and loading of the atmosphere\u00a0 etc.) from the tidal observations\u00a0 by predefined reduction coefficients prior to a Least Squares analysis.<\/li>\n<\/ul>\n<h3><span id=\"15_Polynomial_model\">1.5\u00a0 Polynomial model<\/span><\/h3>\n<ul>\n<li>Uniform polynomial model over the complete tidal record with identical coefficients for all blocks.<\/li>\n<\/ul>\n<h3><span id=\"16_Non_8211_linear_and_additional_harmonics\">1.6\u00a0 Non &#8211; linear and additional harmonics<\/span><\/h3>\n<ul>\n<li>Modelling of non-linear harmonics of tidal origin with known non-linear frequencies by an iterative feed-back analysis procedure.<\/li>\n<li>Modelling of additional harmonics of tidal and\/or non-tidal origin by an iterative feed-back analysis procedure.<\/li>\n<\/ul>\n<h3><span id=\"17_Windows\">1.7\u00a0 Windows<\/span><\/h3>\n<ul>\n<li>Deployment of window functions in combination with the Least Squares technology for improving analysis design and interpretation.<\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Contents1.1\u00a0 Theoretical tides1.1.1 Tide Generating Potential Development (TGP)1.1.2 Earth models1.2\u00a0 Optimal wave grouping1.3\u00a0 Astronomical channels like pole and LOD tides1.4\u00a0 Meteorological regression channels1.5\u00a0 Polynomial model1.6\u00a0 Non &#8211; linear and additional harmonics1.7\u00a0 Windows 1.1\u00a0 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\u2026 <span class=\"read-more\"><a href=\"\/eterna\/?page_id=6073\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":13,"featured_media":0,"parent":10113,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/pages\/6073"}],"collection":[{"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"\/eterna\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6073"}],"version-history":[{"count":42,"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/pages\/6073\/revisions"}],"predecessor-version":[{"id":12903,"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/pages\/6073\/revisions\/12903"}],"up":[{"embeddable":true,"href":"\/eterna\/index.php?rest_route=\/wp\/v2\/pages\/10113"}],"wp:attachment":[{"href":"\/eterna\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}