Coordinate Transformations – Understanding Limitations and Challenges

coordinate systemepsg

In order to apply shapely.affinity.scale (see documentation) I have had to transform a series of geodetic coordinates to projected coordinates, see python – UserWarning: Geometry is in a geographic CRS. Results from 'buffer' are likely incorrect – Stack Overflow and UserWarning: Geometry is in a geographic CRS. Results from 'buffer' are likely incorrect for context

All my coordinates are within a bounding box defined as 35.5, -11.0, 71.5, 31.5 (South, West, North, East) covering most of Europe.

Transformation of e.g. 54.1767° latitude and 7.8911° longitude from EPSG:4326 (WGS 84) to EPSG:4936 (ETRS89) results in X: 3705858.6428144597 and Y: 513643.6629113175. But the reverse transformation results in 0° latitude and 7.8911° longitude! So something is wrong.

Transformation from EPSG:4326 to EPSG:3034 (ETRS89-extended / LCC Europe) and back to EPSG:4326 works just fine.

Both coordinate systems (EPSG:4936 and EPSG:3034) cover the same area (WGS84 bounds: -16.1 32.88, 40.18 84.73) and the coordinates used fall within these bounds.

What limitation of coordinates transformations am I missing?

UPDATE: a Minimal, Reproducible Example in Python

In [1]: import geopandas as gpd 
        import pandas as pd 
        import shapely 

In [2]: point = shapely.Point([7.8911,54.1767]) 

In [3]: gdf = gpd.GeoDataFrame(index=[0], crs="epsg:4326", 
                               geometry=[point]) 

In [4]: # transform point from WGS 84 to ETRS89 
        gdf["geometry"].to_crs(4936)
Out[4]: 0    POINT (3705858.64281 513643.66291)
        Name: geometry, dtype: geometry

In [5]: # transform point from WGS 84 to ETRS89 and back to WGS 84 
        gdf["geometry"].to_crs(4936).to_crs(4326) 
Out[5]: 0    POINT (7.89110 0.00000)
        Name: geometry, dtype: geometry

In [6]: # transform point from WGS 84 to ETRS89-extended 
        gdf["geometry"].to_crs(3034)
Out[6]: 0    POINT (3866814.669 3036011.045)
        Name: geometry, dtype: geometry

In [7]: # transform point from WGS 84 to ETRS89-extended and back to WGS 84 
        gdf["geometry"].to_crs(3034).to_crs(4326) 
Out[7]: 0    POINT (7.89110 54.17670)
        Name: geometry, dtype: geometry

Best Answer

Both EPSG:4326 (WGS 84) and EPSG:3034 (ETRS89-extended / LCC Europe) are 2D cartesian coordinate systems. EPSG:4936 (ETRS89) is a (geocentric) 3D cartesian coordinate system:

Cartesian 3D CS (geocentric). Axes: geocentric X Y Z. Orientations: X and Y in equatorial plane, X positive through intersection with prime meridian, Y through 0°N 90°E. Z axis parallel to mean earth rotation axis and positive towards North Pole. UoM: m.

The transformation of coordinates into a 3D coordinate system requires three parameters. A missing parameter leads to an error during the transformation.

Thanks to mkennedy for pointing me in the right direction!

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