Education: VDatum Standard Procedures

V02: Creating VDatum Transformation Grids

Generation of the Topography of the Sea Surface (TSS) Transformation Grids

The National Geodetic Survey (NGS) has the responsibility of creating the sea surface topography (TSS) transformation grids for the VDatum project areas. These transformation grids provide compensation for the local variations between a mean sea-level surface and the NAVD 88 geopotential surface.  A positive value specifies that the NAVD 88 reference value is further from the center of the Earth than the local mean sea-level surface.

Tidal benchmark elevation information is obtained through the Tidal and Orthometric Elevations tool located on the NGS Geodetic Tool Kit (http://www.ngs.noaa.gov/TOOLS/). Tidal data is obtained from CO-OPS database (http://tidesandcurrents.noaa.gov).  Both tidal benchmark elevation information and tidal data are based on the most recent National Tidal Datum Epochs (NTDE). The most current NTDE is 1983-2001.

At each NGS benchmark location, we have a set of TBMdatum values, which is the elevation at the Tidal Benchmark of a datum relative to MLLW (i.e., datum – MLLW). Also, from the four tidal datum transformation grids: MHHW, MHW, MLW and MLLW (see V02: Creation of the Tidal Datum Transformation Grids), we have a set of VDdatum values, which is the difference between the tidal datum and MSL (i.e., datum – MSL). VDdatum values are interpolated to the location of the tidal benchmark.

For the first step, the residual, R, for each datum is calculated as below:

Rmllw = TBMnavd88 + VDmllw
Rmlw = TBMnavd88 - TBMmlw + VDmlw
Rmhw = TBMnavd88 - TBMmhw + VDmhw
Rmhhw = TBMnavd88 - TBMmhhw + VDmhhw

The four residuals at the benchmark are averaged to produce the mean. Note that this mean is an estimate of the quantity MSL – NAVD88.

Next, a gridded sea surface topography field is generated. The mean residuals at all benchmarks are merged with values of the quantity NAVD88 – MSL at CO-OPS’ water level stations to produce input data for contouring. A mesh covering the entire area of benchmarks and water level stations with a spatial resolution similar to that of the tidal marine grids is created. Breaklines are inserted to represent the influence of land. An initial topography of sea surface transformation grid is generated using the Surfer© software’s minimum curvature algorithm to create a surface that honors the data as closely as possible. The maximum allowed departure value used was 0.0001 meters.  To control the amount of bowing on the interior and at the edges of the grid, an internal and boundary tension value of 0.3 was utilized.  Once the initial TSS transformation grid has been generated, null values are obtained from the marine tidal grids and are inserted to denote the presence of land.

Then the residual R for each datum is calculated again as below:

Rmllw = TBMnavd88 + VDmllw - VDtss
Rmlw = TBMnavd88 - TBMmlw + VDmlw - VDtss
Rmhw = TBMnavd88 - TBMmhw + VDmhw - VDtss
Rmhhw = TBMnavd88 - TBMmhhw + VDmhhw - VDtss

Where VDtss represents the value of the quantity NAVD88 - MSL obtained from the initial TSS grid. VDtss value is interpolated to the location of the tidal benchmark. At this time, a residual Rdatum represents the difference between the observed tidal datum and the datum as computed by the initial TSS grid.

The averaged R at each benchmark should be less than 0.01 m.  If it is not, the input data and grids are checked, appropriate changes are made, and the residual Rdatum are recomputed until the criterion is met.

Quality control was carried out by comparing observed benchmarks values to those predicted. After the TSS is created, it is incorporated into VDatum. For the first test, conversions between NAVD 88 and the tidal datums MLLW, MLW, MHW, and MHHW at tidal benchmarks were computed. All final residual Rdatum values are tabulated and examined.

For the second test, the mean difference between known NAVD 88 to MSL relationships and that predicted by VDatum is computed. The mean is examined and evaluated.