EPSG Dataset :: v12.003

Vertical change by geoid grid difference (NRCan)

Coordinate Operation Method Details [VALID]

Name:

Vertical change by geoid grid difference (NRCan)

Code:

1126

Operation is Reversible:

Yes

Formula:

The relationship between CGVD28 and CGVD2013 gravity-related vertical coordinate reference systems in Canada is available through gridded data files of height differences. These have been derived as the difference between the CGVD28 hybrid geoid height and the CGVD2013 geoid height.

The vertical height difference at a point is first interpolated within the grid of values using biquadratic interpolation. (For many practical purposes bilinear interpolation will give results that are not significantly different). For interpolation within the height differences grid, horizontal positions in the Interpolation CRS are used.

The interpolated value is then applied as a correction parameter (A). The interpolated height difference is subtracted from the height in the source CRS:
H2 = H1 - A1>2
where
H2 = value in the target vertical coordinate reference system.
H1 = value in the source vertical coordinate reference system.
A1>2 is the height difference to be applied for the transformation from CRS 1 to CRS 2.

For the reverse transformation from CRS 2 to CRS 1, the same formula is used but with the sign of the height difference A1>2 reversed:
H1 = H2 - (-A1>2) = H2 + (A1>2)

Care! In the EPSG Dataset, offsets are additive (for the forward transformation). See EPSG Guidance Note 7-2, §1.5 Implementation Notes - Offsets. The CGVD height difference files for Canada give height difference values that must be subtracted. For that reason this method is considered to not use vertical offsets.

Example:

For a point at 49°53'09.293"N, 99°54'41.057"W referenced to NAD83(CSRS)v6 (CRS code 8252) with CGVD28 height of 397.140 metres, to find its CGVD2013(CGG2013a) epoch 2010 height:

First obtain the height differences at each of the surrounding grid nodes by interpolation of the HT2_2010_CGG2013a.byn grid file. Using biquadratic interpolation for 49°53'09.293"N, 99°54'41.057"W, the height difference = 0.382 m.

Then CGVD2013(CGG2013a) epoch 2010 height = 397.140 - 0.382 = 396.758 m.

For the reverse calculation to find the CGVD28 height from CGVD2013(CGG2013a) epoch 2010 height of 396.758 m:

First interpolate the grid as for the forward transformation. Height difference = 0.382 m.

Then CGVD28 height = 396.758 + 0.382 = 397.140 m.

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Geoid model difference file	1063	No	The name of the [path and] file containing the height differences between two geoid model surfaces.
EPSG code for Interpolation CRS	1048	No	The EPSG code for the CRS that should be used to interpolate gridded data.

Meta Data

Remarks:

Information Source:

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

Data Source:

EPSG

Revision Date:

January 15, 2024

Change ID:

[2023.054]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.