EPSG:9665

This transformation involves the application of a height difference interpolated from a height correction model. The model provides height difference values at the nodes on a regular grid of latitude and longitude intersection points. The geodetic latitude and longitude used to interpolate within the grid are not affected by this transformation.

The grid is referenced to a specific geographic CRS (the horizontal component of the source CRS) and interpolation must be made in the latitude and longitude of this system.

Calculation of the height difference is achieved through a bi-linear interpolation of the grid, using the latitude and longitude of the point. This step provides the height correction (C) of the target datum above the ellipsoid of the source Geographic 3D CRS. C differs from the geoid-ellipsoid separation N because a vertical datum is a realisation of the geoid surface, not the geoid itself.

Then:
           H = h - C

where h = the height above the ellipsoid in the source geographic 3D CRS
and   H = the gravity-related height in the target vertical CRS.

The method is not reversible because the gravity-related height is 1-dimensional and not associated with a horizontal CRS.