# EPSG:1112

## Vertical Offset by Grid Interpolation (NRCan byn)

### Attributes

Data source: EPSG

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

Revision date: 2022-06-29

### Formula

```The relationship between two gravity-related coordinate reference systems may be available through gridded data files of offsets (sometimes called height differences).

The vertical offset at a point is first interpolated within the grid of values using bi-linear interpolation. For interpolation within the offset grid, horizontal positions in the Interpolation CRS are used.

The interpolated value is then applied as a correction parameter A. The interpolated offset is added to 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 offset to be applied for the transformation from CRS 1 to CRS 2. Its value for the forward calculation is the value of the origin of the source CRS 1 in the target CRS 2.

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

Care! In the EPSG Dataset, offsets are additive (for the forward transformation). See EPSG Guidance Note 7-2, Implementation Notes - 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 offsets at each of the surrounding grid nodes by interpolation of the HT2_2010_CGG2013a.byn grid file. Then using biquadratic interpolation for 49°53'09.293"N, 99°54'41.057"W, the offset = -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. Offset = -0.382 m.

Then CGVD28 height = 396.758 - (-0.382) = 397.140 m.```