VDatum Transformation Grid Formats

Interpolation Overview

As you traverse various paths along the VDatum roadmap, both parameter transformations and grid based interpolation might be utilized for transforms. 3-D datums provide the foundation for accurate determination of ellipsoidal heights and employ parameter transforms contained within HTDP. Orthometric datums are those that employ the Earth's gravity field as their datum and Tidal datums are those based on tidally-derived surfaces of high or low water and both of these employ grids for the transform. In order to provide transformation values at any point within the gridded area, it is necessary to interpolate between grid-defined points. The following interpolation methods are utilized in VDatum.

Bilinear interpolation: Bilinear interpolation is the use of quadratic functions in two dimensions, to interpolate a value at any location, from some given grid of values. In order to provide a unique solution therefore, bilinear interpolation relies upon the nearest 2 × 2 set of grid points to the point of interpolation (POI). Inverse distance weighted interpolation method is used when there is more than one Null point.

Biquadratic Interpolation: As its name implies, biquadratic interpolation is the use of quadratic functions in two dimensions, to interpolate a value at any location, from some given grid of values. In order to provide a unique solution therefore, biquadratic interpolation relies upon the nearest 3 × 3 set of grid points to the point of interpolation (POI).

Datum Transformation Grid (.GTX) Overview

Coordinate readjustments in VDatum require datum transformation grids for their interpolation in VDatum. A datum transformation grid is a regular, rectangular array of height values that comprised of evenly spaced rows and columns. The intersection of a row and a column is called a grid point. Rows contain grid points with the same latitude coordinate, and columns contain grid points with the same longitude coordinate. The height of the surface at each grid point is defined by the height value assigned to that point.

The height values are stored in order starting with the minimum longitude (column) and minimum latitude (row) coordinates. The first height value in the datum transformation grid file corresponds to the lower left corner of the map. The second height value is the next adjacent grid point in the same row, i.e. same latitude (row) coordinate but the next higher longitude (column) coordinate. When the maximum longitude is reached in the row, the list of height values continues with the next higher row (latitude coordinate) and minimum longitude coordinate, until all the rows of height values have been included.

An example of the datum transformation grid order for a 4 x 4 grid is: 

All transformation grids are horizontally registered in the NAD 83 (2011). Given the accuracy and granularity of these grids, any WGS 84 or ITRF georeferenced grid can be considered identical to NAD 83 (NSRS2011/2007/FBN/HARN). If source datum transformation data are georeferenced in NAD 27 or NAD 83 (1986), they must be horizontally transformed into NAD 83 (NSRS2011/2007/FBN/HARN) or an equivalent prior to grid generation.

All height values are in meters.

NADCON 5.0 release 20160901, the horizontal transformation model between NAD 27, NAD 83 (1986) and NAD 83 (HARN), use similar grids to express latitude and longitude shifting. NADCON 5.0 shifting values are in seconds of arc (or arc second).

Files with the [.GTX] extension are VDatum transformation grid files. Prior VDatum 2.x, transformation grids are in ASCII format which practically limits the size of a grid file based on the amount of available computer memory. To bypass the size/memory limits, transformation grids are now in binary format which shares a similar layout with the ASCII format.

Description of Datum Transformation Grid Contents (units of meter unless noted)

ASCII Transformation Grid File Format

ASCII transformation grid files [.GTX] contain one header line that provides information about the size and resolutions of the grid, followed by a list of height values. The header fields within ASCII grid files are space delimited. Only one height value is provided in each line after the header line.

The general format of an ASCII transformation grid file is: 

Lower-left-Latitude Lower-left-Longitude deltaLatitude deltaLongitude nRows nColumns
the height value of the grid point #1
the height value of the grid point #2
...

where: 

The following example shows the beginning of a transformation grid file in ASCII format, including the header line and height values of grid points on the first row (the bottom row) of the grid. This grid file is started from 42.25 degrees Lat and 276.75 degrees Long, comprised of 11 rows height by 12 columns. Each grid point is spaced by 0.05 degrees on Latitude axis and 0.025 degrees on Longitude axis. The first height value (.8880 meters) corresponds to the height value of the lower left corner of the grid. The following values correspond to the increasing longitude position along the bottom row of the grid file.

42.25000000000000 276.75000000000000 .05000000000000 .02500000000000 11 12
.88880
-88.88880
-88.88880
-88.88880
-88.88880
-88.88880
-88.88880
-88.88880
-88.88880
-88.88880
-.00542
-.00560
...