# Vertical Offset And Slope¶

New in version 9.1.0.

The Vertical Offset And Slope offsets transformation adds an offset to an orthometric height, taking account a constant offset and a inclinated plane, defined by its slope along latitude and longitude axis.

 Alias vertoffset Domain 3D Input type Geodetic coordinates (horizontal), meters (vertical) output type Geodetic coordinates (horizontal), meters (vertical)

It is documented as coordinate operation method code 1046 in the EPSG dataset ([IOGP2018]). It is typically used in Europe, to relate national vertical systems to pan-European vertical systems (EVRF200, EVRF2007).

## Examples¶

Vertical offset from LN02 height to EVRF2000 height with horizontal coordinates in ETRS89:

+proj=vertoffset +lat_0=46.9166666666666666 +lon_0=8.183333333333334 \
+dh=-0.245 +slope_lat=-0.210 +slope_lon=-0.032 +ellps=GRS80


## Parameters¶

### Required¶

+lat_0=<value>

Latitude of origin of the inclinated plane.

+lon_0=<value>

Longitude of origin of the inclinated plane

+dh=<value>

Offset in height, expressed in meter, to add.

+slope_lat=<value>

Slope parameter in the latitude domain, expressed in arc-seconds.

+slope_lon=<value>

Slope parameter in the longitude domain, expressed in arc-seconds.

+ellps=<value>

The name of a built-in ellipsoid definition.

See Ellipsoids for more information, or execute proj -le for a list of built-in ellipsoid names.

Defaults to “GRS80”.

## Formula¶

The $$Z_{dest}$$ destination elevation is obtained from the $$Z_{src}$$ source elevation with:

\begin{align} Z_{dest} = Z_{src} + \left( dh + slope_{lat} * {\rho}_0 * (\phi - {\phi}_0) + slope_{lon} * {\nu}_0 * (\lambda - {\lambda}_0) * cos(\phi) \right) \end{align}

where:

• $$dh$$, $$slope_{lat}$$ and $$slope_{lon}$$ are the above mentioned parameters

• $${\lambda}_0$$, $${\phi}_0$$ is the longitude, latitude of the point of origin of the inclinate plane (+lon_0, +lat_0)

• $$\lambda$$, $$\phi$$ is the longitude, latitude of the point to evaluate

• $${\rho}_0$$ is the radius of curvature of the meridian at latitude $${\phi}_0$$

• $${\nu}_0$$ is the radius of curvature on the prime vertical (i.e. perpendicular to the meridian) at latitude $${\phi}_0$$

The reverse formula is:

\begin{align} Z_{src} = Z_{dest} - \left( dh + slope_{lat} * {\rho}_0 * (\phi - {\phi}_0) + slope_{lon} * {\nu}_0 * (\lambda - {\lambda}_0) * cos(\phi) \right) \end{align}