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

<strong>Nodal tide components for the PSMSL annual and monthly dataset (preliminary)</strong> 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. <strong>Authors and contact</strong> 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. <strong>Files</strong> You can find the following files in this dataset. <code>monthlymean_gtsm_psmsl-{id}.csv</code>: monthly tidal corrections for mean sea level. <code>yearlymean_gtsm_psmsl-{id}.csv</code>: annual tidal corrections for the mean sea level. <code>yearlymeanOLS_gtsm_psmsl-{id}.csv</code>: annual tidal corrections based on a harmonic analysis through the reanalysis data (see details below). <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. 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. 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]. <strong>Data specific information</strong> The file <code>monthlymean_gtsm_psmsl-{id}.csv</code> contains the following columns: - <code>time [year-month]</code> : year-month for which the mean tidal level is determined - <code>sea_surface_height_due_to_tide [m]</code>: mean sea surface level due to tidal waves [m] The file <code>yearlymean_gtsm_psmsl-{id}.csv</code> contains the following columns: - <code>time [year]</code>: year for which the mean tidal level is determined - <code>sea_surface_height_due_to_tide [m]</code>: mean sea surface level due to tidal waves [m] The file <code>yearlymeanOLS_gtsm_psmsl-{id}.csv</code> contains the following columns: - <code>time [year]</code>: year for which the mean tidal level is determined - <code>sea_surface_height_due_to_tide_fitted [m]</code>: mean sea surface level due to tidal waves, harmonic fit [m] The file <code>df_OLSmodelstats_year.csv</code> contains the following columns: <code>longitude [degrees east]</code>: longitude of the station <code>latitude [degrees north]</code>: latitude of the station <code>station_name</code>: station name <code>nodal tide U [m]</code>: linearized fit of the nodal cycle (A/U/cos term) (relative to 1970) [m] <code>nodal tide V [m]</code>: linearized fit of the nodal cycle (B/V/sin term) (relative to 1970) [m] <code>nodal amplitude [m]</code>: amplitude of the fitted nodal cycle, sqrt(A<strong>2 + B</strong>2) [m] <code>nodal phase [radians since 1970-01-01]</code>: phase of the fitted nodal cycle arctan2(B, A) [rad, epoch 1970] <code>mean sea surface height of nodal fit [m]</code>: mean tidal level over the fitted time window [m] <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] <code>nodal amplitude of equilibrium tide [m]</code>: equilibrium amplitude of the nodal tide [m] <strong>Methods</strong> 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. The equilibrium ampltiude is computed as: <pre><code>abs(0.69 * 20 * (3 * sin(deg2rad(lat))**2 - 1)) / 1000</code></pre> This assumes an all water, elastic earth, and no self attraction. 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. 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]. The results have not been validated or published, so please use this dataset with caution. See the details in the section preliminary results. <strong>Preliminary results</strong> These are preliminary results, intended for evaluation with other scientists. Make sure you take into account the following: 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. The following regions are not reliable: Black Sea, due to a limited topological relation with the rest of the grid. These stations are excluded. Regions in inlets have not been validated 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). The phase of the nodal tide is not yet validated. Some stations have deviating mean sea levels. A few examples: psmsl-173: station in the river mound the St. Lawrence River in Quebec. Not enough resolution psmsl-1067: Anchorage in Alaska, in an inlet psmsl-495: inlet psmsl-1908: bathymetry/bridge psmsl-2285: bathymetry resolution/bridge 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. <strong>Sharing and Access information</strong> This dataset is available under a CC-BY-SA license [3]. See the link below for details.<br> This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Please make sure you refer to the preliminary status of this dataset if you use it. [0] https://www.psmsl.org [1] https://doi.org/10.2112/JCOASTRES-D-11-00169.1 [2] https://doi.org/10.2112/JCOASTRES-D-11A-00023.1 [3] http://creativecommons.org/licenses/by-sa/4.0/**PSMSL年/月均数据集（预发布版）的节点潮汐分量** 本预发布数据集涵盖永久平均海平面服务（Permanent Service for Mean Sea Level, PSMSL）数据集内验潮站的平均海平面潮汐分量。上述文件可用于剥离平均海平面的长期潮汐信号。 **作者与联系方式** 本数据集由Jelmer Veenstra、Martin Verlaan、Fedor Baart与Willem Stolte共同构建。如需了解更多信息，可联系Jelmer Veenstra或Fedor Baart。 **数据集文件说明** 本数据集包含以下文件： - `monthlymean_gtsm_psmsl-{id}.csv`：用于平均海平面的月度潮汐订正数据 - `yearlymean_gtsm_psmsl-{id}.csv`：用于平均海平面的年度潮汐订正数据 - `yearlymeanOLS_gtsm_psmsl-{id}.csv`：基于再分析数据的调和分析（harmonic analysis）得到的年度潮汐订正数据（详见下文） - `df_OLSmodelstats_year.csv`：所有验潮站调和分析的相位与振幅汇总表，同时包含平衡潮汐振幅 所有文件均采用逗号作为字段分隔符、句点作为小数分隔符的CSV格式存储。年度数据的时间格式为`YYYY`，月度数据的时间格式为`YYYY-MM`。`df_OLSmodelstats_year.csv`同时包含本数据集覆盖的所有验潮站列表，相关验潮站的更多信息可查阅[1]。 **数据详情说明** 1. `monthlymean_gtsm_psmsl-{id}.csv`包含以下字段： - `time [year-month]`：计算平均潮汐水位对应的年-月时间戳 - `sea_surface_height_due_to_tide [m]`：由潮汐波引起的平均海平面高度（单位：米） 2. `yearlymean_gtsm_psmsl-{id}.csv`包含以下字段： - `time [year]`：计算平均潮汐水位对应的年份 - `sea_surface_height_due_to_tide [m]`：由潮汐波引起的平均海平面高度（单位：米） 3. `yearlymeanOLS_gtsm_psmsl-{id}.csv`包含以下字段： - `time [year]`：计算平均潮汐水位对应的年份 - `sea_surface_height_due_to_tide_fitted [m]`：通过调和拟合得到的潮汐波平均海平面高度（单位：米） 4. `df_OLSmodelstats_year.csv`包含以下字段： - `longitude [degrees east]`：验潮站经度（东经度数） - `latitude [degrees north]`：验潮站纬度（北纬度数） - `station_name`：验潮站名称 - `nodal tide U [m]`：节点潮汐周期的线性拟合项（A/U/余弦项，以1970年为基准），单位：米 - `nodal tide V [m]`：节点潮汐周期的线性拟合项（B/V/正弦项，以1970年为基准），单位：米 - `nodal amplitude [m]`：拟合得到的节点潮汐周期振幅，计算公式为√(A²+B²)，单位：米 - `nodal phase [radians since 1970-01-01]`：拟合得到的节点潮汐周期相位，采用arctan2(B,A)计算，以1970-01-01为纪元，单位：弧度 - `mean sea surface height of nodal fit [m]`：拟合时段内的平均潮汐水位，单位：米 - `nodal amplitude fitted with nodal epoch [m]`：以节点潮汐相位起始时刻为纪元的拟合节点潮汐振幅，需注意此处振幅可能为负值，单位：米 - `nodal amplitude of equilibrium tide [m]`：节点平衡潮汐振幅，单位：米 **研究方法** 本数据集通过运行潮汐模型GTSM v4.0，开展了19年的模拟计算。本次多十年潮汐再分析工作可实现潮汐分量与其他海平面波动的分离，本计算的目的是对验潮站的年、月均记录进行该潮汐分量的订正。相关讨论可查阅文献[1,2]。 平衡潮汐振幅的计算公式如下： `abs(0.69 * 20 * (3 * sin(deg2rad(lat))**2 - 1)) / 1000` 该公式假设地球为全水覆盖的弹性球体，且不考虑自吸引效应。 本次模拟中，所有约400个潮汐强迫均处于激活状态，因此计算结果同时包含间接非线性效应，例如M2分潮振幅自身的节点调制作用，这使得计算结果可偏离平衡潮汐。模拟中纳入了潮汐势能、固体潮订正（通过洛夫数（Love numbers）实现）以及自吸引与负荷效应。 本数据集采用普通最小二乘法（ordinary least squares）拟合节点潮汐的振幅与相位，相关分析细节可查阅配套脚本[3]。本数据集的结果尚未经过验证或正式发表，使用时请谨慎，相关说明详见“预发布结果”章节。 **预发布结果说明** 本数据集为预发布结果，仅供科研同行评估使用。请注意以下事项： 1. 本结果基于GTSM 4.0模型生成，我们计划基于GTSM 4.1推出更新版本。GTSM 4.1将配备更完善的内部潮汐模型，有望整体提升再分析结果的精度。 2. 以下区域的结果不可靠：黑海区域，因其与网格其余部分的拓扑关联有限，相关验潮站已被排除；潮道区域的结果尚未经过验证。 3. 本次再分析得到的振幅较平衡潮汐预期值偏低（约为预期值的1/2），目前正对该现象的成因开展研究（可考虑洛夫数、自吸引效应等因素）。 4. 节点潮汐的相位尚未经过验证。 部分验潮站的平均海平面存在异常，举例如下： - psmsl-173：位于魁北克省圣劳伦斯河河口的验潮站，网格分辨率不足 - psmsl-1067：阿拉斯加州安克雷奇潮道区域的验潮站 - psmsl-495：潮道区域验潮站 - psmsl-1908：受水深地形/桥梁影响的验潮站 - psmsl-2285：受水深地形分辨率/桥梁影响的验潮站 通用说明：狭窄潮道及内河验潮站的结果精度不足。在后续更新版本中，我们可尝试采用潮道外侧的网格单元进行计算——狭窄潮道内外的潮汐特征差异显著。 **共享与使用说明** 本数据集采用知识共享署名-相同方式共享（CC-BY-SA）协议授权发布[3]，详细授权条款可查阅以下链接。本作品采用知识共享署名-相同方式共享4.0国际许可协议进行许可。如您使用本数据集，请务必注明其预发布状态。 [0] https://www.psmsl.org [1] https://doi.org/10.2112/JCOASTRES-D-11-00169.1 [2] https://doi.org/10.2112/JCOASTRES-D-11A-00023.1 [3] http://creativecommons.org/licenses/by-sa/4.0/