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Nodal tide components for the PSMSL annual and monthly dataset (preliminary)

<p><strong>Nodal tide components for the PSMSL annual and monthly dataset (preliminary)</strong></p> <p>This preliminary dataset contains the tidal component for the mean sea level for the tide gauges in the Permanent Service for Mean Sealevel dataset. These files can be used to subtract the long term tide of the mean sea level.</p> <p><strong>Authors and contact</strong></p> <p>This dataset is created by Jelmer Veenstra, Martin Verlaan, Fedor Baart, and Willem Stolte. You can contact Jelmer Veenstra or Fedor Baart for more information.</p> <p><strong>Files</strong></p> <p>You can find the following files in this dataset.</p> <ul> <li><code>monthlymean_gtsm_psmsl-{id}.csv</code>: monthly tidal corrections for mean sea level.</li> <li><code>yearlymean_gtsm_psmsl-{id}.csv</code>: annual tidal corrections for the mean sea level.</li> <li><code>yearlymeanOLS_gtsm_psmsl-{id}.csv</code>: annual tidal corrections based on a harmonic analysis through the reanalysis data (see details below).</li> <li><code>df_OLSmodelstats_year.csv</code>: an overview of the phase and amplitude of the harmonic analysis of all the stations, also includes the equilibrium tidal amplitude.</li> </ul> <p>All files are stored in <code>.csv</code> files, using a <code>,</code> as field separator and <code>.</code> as decimal separator. Time is stored as <code>YYYY</code> for the annual series and as <code>YYYY-MM</code> for the monthly series.</p> <p>The file <code>df_OLSmodelstats_year.csv</code> also contains the list of all stations for which we provide information. More information on these stations can be found at [1].</p> <p><strong>Data specific information</strong></p> <p>The file <code>monthlymean_gtsm_psmsl-{id}.csv</code> contains the following columns:</p> <ul> <li>- <code>time [year-month]</code> : year-month for which the mean tidal level is determined</li> <li>- <code>sea_surface_height_due_to_tide [m]</code>: mean sea surface level due to tidal waves [m]</li> </ul> <p>The file <code>yearlymean_gtsm_psmsl-{id}.csv</code> contains the following columns:</p> <ul> <li>- <code>time [year]</code>: year for which the mean tidal level is determined</li> <li>- <code>sea_surface_height_due_to_tide [m]</code>: mean sea surface level due to tidal waves [m]</li> </ul> <p>The file <code>yearlymeanOLS_gtsm_psmsl-{id}.csv</code> contains the following columns:</p> <ul> <li>- <code>time [year]</code>: year for which the mean tidal level is determined</li> <li>- <code>sea_surface_height_due_to_tide_fitted [m]</code>: mean sea surface level due to tidal waves, harmonic fit [m]</li> </ul> <p>The file <code>df_OLSmodelstats_year.csv</code> contains the following columns:</p> <ul> <li><code>longitude [degrees east]</code>: longitude of the station</li> <li><code>latitude [degrees north]</code>: latitude of the station</li> <li><code>station_name</code>: station name</li> <li><code>nodal tide U [m]</code>: linearized fit of the nodal cycle (A/U/cos term) (relative to 1970) [m]</li> <li><code>nodal tide V [m]</code>: linearized fit of the nodal cycle (B/V/sin term) (relative to 1970) [m]</li> <li><code>nodal amplitude [m]</code>: amplitude of the fitted nodal cycle, sqrt(A<strong>2 + B</strong>2) [m]</li> <li><code>nodal phase [radians since 1970-01-01]</code>: phase of the fitted nodal cycle arctan2(B, A) [rad, epoch 1970]</li> <li><code>mean sea surface height of nodal fit [m]</code>: mean tidal level over the fitted time window [m]</li> <li><code>nodal amplitude fitted with nodal epoch [m]</code>: amplitude of the fitted nodal tide with epoch at the start of the phase of the nodal tide. Note that the amplitude here can be negative. [m]</li> <li><code>nodal amplitude of equilibrium tide [m]</code>: equilibrium amplitude of the nodal tide [m]</li> </ul> <p><strong>Methods</strong></p> <p>To generate this dataset we have run a tidal model (GTSM v4.0) for 19 years. This multi-decadal reanalysis of tides allows separating the tidal component from other sea-level fluctuations. The purpose of this computation is to correct yearly mean and monthly mean tide gauge records for this tide constituent. See [1, 2] for a discussion on this topic.</p> <p>The equilibrium ampltiude is computed as:</p> <pre><code>abs(0.69 * 20 * (3 * sin(deg2rad(lat))**2 - 1)) / 1000</code></pre> <p>This assumes an all water, elastic earth, and no self attraction.</p> <p>In this simulation, all tidal forcings (~400) are active. Thus the estimates also contain indirect non-linear effects, such as the nodal modulation on the amplitude of M2 interacting with itself. This allows the computation to deviate from the equilibrium tide. The tidal potential, corrections for solid earth tide (through Love numbers), and self attraction and loading are included.</p> <p>Using this dataset we fit, using an ordinary least squares approach, the nodal tidal amplitude, and phase. Details of this analysis can be found in the corresponding notebook [3].</p> <p>The results have not been validated or published, so please use this dataset with caution. See the details in the section preliminary results.</p> <p><strong>Preliminary results</strong></p> <p>These are preliminary results, intended for evaluation with other scientists. Make sure you take into account the following:</p> <ul> <li> <p>These results are based on GTSM 4.0, we expect to create an updated version based on 4.1. Version 4.1 should have a better internal tide model, which should improve reanalysis results in general.</p> </li> <li> <p>The following regions are not reliable:</p> <ul> <li>Black Sea, due to a limited topological relation with the rest of the grid. These stations are excluded.</li> <li>Regions in inlets have not been validated</li> </ul> </li> <li> <p>The reanalysis amplitude is lower than expected from equilibrium tide (about a factor 2 lower). Research into the cause of this is pending (love numbers, self attraction can be considered).</p> </li> <li> <p>The phase of the nodal tide is not yet validated.</p> </li> <li> <p>Some stations have deviating mean sea levels. A few examples:</p> </li> <li> <p>psmsl-173: station in the river mound the St.&nbsp;Lawrence River in Quebec. Not enough resolution</p> </li> <li> <p>psmsl-1067: Anchorage in Alaska, in an inlet</p> </li> <li> <p>psmsl-495: inlet</p> </li> <li> <p>psmsl-1908: bathymetry/bridge</p> </li> <li> <p>psmsl-2285: bathymetry resolution/bridge</p> </li> </ul> <p>General remark: resolution in narrow tidal inlets and stations up rivers are not accurate. In an updated version we might be able to use cells just outside the inlet. Tide in narrow inlets can be quite different from outside.</p> <p><strong>Sharing and Access information</strong></p> <p>This dataset is available under a CC-BY-SA license [3]. See the link below for details.<br> This work is licensed under a <a href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike 4.0 International License</a>.</p> <p>Please make sure you refer to the preliminary status of this dataset if you use it.</p> <p>[0] https://www.psmsl.org</p> <p>[1] https://doi.org/10.2112/JCOASTRES-D-11-00169.1</p> <p>[2] https://doi.org/10.2112/JCOASTRES-D-11A-00023.1</p> <p>[3] http://creativecommons.org/licenses/by-sa/4.0/</p>