# Gridshifting¶

Sometimes it is simpler to define a transformation as a gridded model of displacements rather than a mathematical model. This approach, pioneered by the US National Geodetic Survey in their 1980s era transformation from the old NAD27 datum to the (back then) new NAD83, has become increasingly popular as disk space and CPU cycles have gotten cheaper.

Gridded models of displacements offer the ability to make local adjustments that are not possible with e.g. a Helmert transformation. This fact is especially leveraged in transformations of heights since the geoid is too bumpy to retain enough detail with a simple mathematical definition.

The main problem with grid shifting is availability of the grids needed for a given transformation. The PROJ package requires that the PROJ-data package is installed alongside it.

Download the gie file for the exercise: `gridshift.gie`.

## Exercises 1. Horizontal gridshifting¶

In this exercise we will apply a horizontal grid shift as it is done in the transformation from the German DHDN to ETRS89 transformation.

Define the operation that converts from DE_DHDN to ETRS89 using a gridshift.

Hint

Hint

Find the relevant grid name by inspecting the output of

`projinfo -s DHDN -t ETRS89 -o WKT2_2019`

Note that two operations are returned, look for the one which uses the "NTv2" method.

```operation   <your answer here>
tolerance   1 mm

accept      13.0            52.0            0.0
expect      12.9983317082   51.9986488216   0.0
```

## 2. Vertical gridshifting¶

The most common use case for vertical grid shifts is transformation from ellipsoidal heights to physical heights. In most cases this is equivalent to applying an offset from a geoid model, which is exactly what we will do in this exercise.

Set up an operation that transforms ellipsoidal heights to physical heights using the EGM96 model.

Hint

Hint

The relevant grid name is "us_nga_egm96_15.tif"

```operation   <your answer here>
tolerance   1 mm

accept      13.0            52.0          100.0
expect      13.0            52.0           58.1917
```