# EPSG:9657 DEPRECATED

## Vertical Offset and Slope

### Attributes

Data source: OGP

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

Revision date: 2004-04-14

Remarks: This transformation allows calculation of height in the target system by applying the parameter values to the height value of the point in the source system.

#### Export

Definition: OGP XML

```<?xml version="1.0" encoding="UTF-8"?>
<epsg:informationSource>EPSG guidance note #7-2, http://www.epsg.org</epsg:informationSource>
<epsg:revisionDate>2004-04-14</epsg:revisionDate>
<epsg:changes>
</epsg:changes>
<epsg:isDeprecated>true</epsg:isDeprecated>
<epsg:isOperationReversible>true</epsg:isOperationReversible>
<epsg:example>For coordinate transformation LN02 to EVRF2000 (1)

Ordinate 1 of evaluation point: 46deg 55min N = 0.818850307 	radians
Ordinate 2 of evaluation point: 8deg 11min E of Greenwich = 0.142826110 	radians
Transformation Parameters:
A = -0.245m
IncLat = -0.210"  = -0.000001018 	radians
IncLong = -0.032"  = -0.000000155 	radians

Consider a point having a gravity-related height in the LN02 system (Hs) of 473.0m and with horizontal coordinates in the ETRS89 geographical coordinate reference system of:
ETRS89 latitude: 47deg 20 min N = 0.826122513 	radians
ETRS89 longitude: 9 deg 40min E of Greenwich = 0.168715161 	radians

Then rhoO = 6369526.88 m
IncLat term = -0.047 m
nuO = 6389555.64  m
incLong term = -0.017 m
whence EVRF2000 height (Ht) = 473.0 +(-0.245) + (-0.047) + (-0.017) = 472.690 m.</epsg:example>
<gml:identifier codeSpace="OGP">urn:ogc:def:method:EPSG::9657</gml:identifier>
<gml:name>Vertical Offset and Slope</gml:name>
<gml:remarks>This transformation allows calculation of height in the target system by applying the parameter values to the height value of the point in the source system.</gml:remarks>
<gml:formula>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.

In Europe, national height systems are related to the pan-European height system through three transformation parameters and the formula:

Ht = Hs + A + [IncLat * rhoO * (Lat – LatO)] + [IncLong * nuO * (Long – LongO) * cos(Lat)]

where
Ht = gravity-related height value in the target vertical coordinate reference system.
Hs = gravity-related height value in the source vertical coordinate reference system.
A is the value of the vertical offset to be applied.
IncLat is the value in radians of the inclination parameter in the latitude domain, i.e. in the plane of the meridian, derived at an evaluation point with coordinates of LatO , LongO.
IncLon is the value of the inclination parameter in the longitude domain, i.e. perpendicular to the plane of the meridian.
rhoO is the radius of curvature of the meridian at latitude LatO, where rhoO = a(1 – e^2)/(1 – e^2 * sin^2(LatO))^1.5
nuO is the radius of curvature on the prime vertical (i.e. perpendicular to the meridian) at latitude LatO, wh		ere nuO = a /(1 – e^2 * sin^2(LatO))^0.5
Lat , Long are the horizontal coordinates of the point in the ETRS89 coordinate reference system, in radians.
LatO , LongO are the coordinates of the evaluation point in the ETRS89 coordinate reference system, in radians.

The horizontal location of the point must always be given in ETRS89 terms. Care is required where compound coordinate reference systems are in use: if the horizontal coordinates of the point are known in the local CRS they must first be transformed to ETRS89 values. The method is reversible.</gml:formula>
<gml:sourceDimensions>1</gml:sourceDimensions>
<gml:targetDimensions>1</gml:targetDimensions>