# EPSG:1101

## Vertical Offset by Grid Interpolation (PL txt)

### Attributes

Data source: EPSG

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

Revision date: 2021-03-18

### 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 coordinate transformation: NZVD2016 height to Dunedin 1958 height (2), code 9314:

For a point at 44.42°S, 168.92°E (using CRS code 4167, NZGD2000, for interpolation) with NZVD2016 height of 50.000 metres, to find its Dunedin 1958 height:

First obtain the offsets at each of the surrounding grid nodes:
NW corner 44.4000°S, 168.9000°E, offset = 0.3028m
NE corner 44.4000°S, 168.9333°E, offset = 0.3029m
SE corner 44.4333°S, 168.9333°E, offset = 0.3055m
SW corner 44.4333°S, 168.9000°E, offset = 0.3051m

Then using bi-linear interpolation for 44.42°S, 168.92°E, offset = 0.304m

Then Dunedin 1958 height = 50.000 + 0.304 = 50.304m.

For the reverse calculation to find the NZVD2016 height from a point with Dunedin 1958 height of 50.304m:

First obtain the offsets at each of the surrounding grid nodes again using coordinates referenced to NZGD2000 for interpolation:
NW corner 44.4000°S, 168.9000°E, offset = 0.3028m
NE corner 44.4000°S, 168.9333°E, offset = 0.3029m
SE corner 44.4333°S, 168.9333°E, offset = 0.3055m
SW corner 44.4333°S, 168.9000°E, offset = 0.3051m

Then using bi-linear interpolation for 44.42°S, 168.92°E, offset = 0.304m

Then NZVD2016 height = 50.304 - 0.304 = 50.000m.```