EPSG

EPSG guidance note #7-2, http://www.epsg.org

2018-02-16

Transformation from a Geographic 3D CRS to a Compound CRS consisting of a Geographic 2D CRS and a Vertical CRS, or vice versa. The Geographic 3D and the Geographic 2D CRS must be based on the same Geodetic Datum.

This is a complex, multi-step transformation, involving the application of a geoid height difference interpolated at a point in a "geoid model". The geoid model should be available as a regular grid of latitude and longitude with the height of the geoid above the ellipsoid at each grid node. Only the height is affected by this transformation; the geodetic latitude and longitude are not. The transformation involves the following sequence of steps: · Selection of a subset of the geoid file covering the extent of the points to be transformed. · If the geoid file is not based on the source or target CRS, it needs to be transformed first. This involves transformation of the chosen subset of the geoid file from its orignal Geographic 3D CRS to the Geographic 3D CRS that is the source or the target of this transformation. · Calculation of the height of the geoid above the ellipsoid ("geoid undulation") at the relevant point(s). This is achieved through a bi-linear interpolation of the geoid undulation, using the latitude and longitude to locate the point in the sub-grid. This step results in the height of the geoid above the ellipsoid (N) of the Geographic 3D CRS, whether source or target. · At each point, the application of the calculated geoid undulation to the height to be transformed. H=h-N for Geographic3D to Geographic2D+GravityRelatedHeight h=H+N for Geographic2D+GravityRelatedHeight to Geographic3D where h = the ellipsoidal height (height above the ellipsoid in a geographic 3D CRS) and H = the gravity-related height (vertical CRS) component of the compound CRS.