EPSG:1083

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

This is a multi-step transformation involving the transformation of a geographic 3D CRS to a compound CRS comprising of a geographic 2D CRS horizontal component and a 1D vertical CRS. It is a requirement of the method that the geographic 2D CRS is the horizontal subset of the geographic 3D CRS. Only the height is affected by this transformation; the geodetic latitude and longitude are not. 

The height involves the application of a geoid height difference interpolated at a point in a "geoid model" consisting of grid of latitude and longitude with the height of the geoid above the ellipsoid at each grid node. 

The forward transformation from geographic 3D φλh to compound (φλ + H) involves the following sequence of steps:
1) apply a Geographic3D to 2D conversion (method 9659, §4.1.4) to convert the geographic 3D coordinates φλh to geographic 2D coordinates referenced the interpolation CRS φλ.
2)  use φλ to interpolate the geoid model for N.
3)  then H = h - N
The compound CRS coordinates (φλ + H) are from steps 1 and 3.

Reverse transformation from compound (φλ + H) to geographic 3D φλh:
1)  Use the horizontal component of the compound CRS (φλ) to the interpolate geoid model for N.
2)  h = H + N
3) In theory, convert φλ to φλh (using the reverse of method 9659, §4.1.4). Theoretically this is indeterminate and requires an assumption about ellipsoidal height. But here use h from step 2, which is the correct value. In practice, geographic 3D coordinates φλh are obtained by combining φλ from step1 with h from step 2. The combination of the coordinate tuples replaces the Geographic2D to 3D conversion.