3D_CRS_Transformation_Resources

A centralized repository for resources, documentation and code samples to help people navigate the infinitely confusing, complex, but very important topic of 3D coordinate reference system (CRS) transformations when combining geospatial datasets.

Background

Awesome ICESat-2 Hackweek 2022 Tutorial from Tyler, Hannah and Scott: https://icesat-2-2022.hackweek.io/tutorials/geospatial/geospatial-advanced.html?highlight=datum
NSIDC notebook on iceflow tool (Kevin Beam) for combining (ICESat, Operation IceBridge and ICESat-2): https://github.com/nsidc/NSIDC-Data-Tutorials/blob/main/notebooks/iceflow/corrections.ipynb
David's GDA module on CRS and projections: https://uwgda-jupyterbook.readthedocs.io/en/latest/modules/04_Vector1_Geopandas_CRS_Proj/04_Vector1_Geopandas_CRS_Proj_prep.html

More resources specific to North America

https://geodesy.noaa.gov/corbin/class_description/NGS_Video_Library.shtml
- What are Geodetic Datums?
- How Were Geodetic Datums Established?
- What Is the Status of Today’s Geodetic Datums?
- What’s Next for Geodetic Datums?
https://www.meted.ucar.edu/oceans/navy_geodesy/
PSU Course GPS and GNSS for Geospatial Professionals (Lesson 5): https://www.e-education.psu.edu/geog862/node/1669
https://www.dnr.wa.gov/publications/eng_plso_state_plane_coord_refresher.pdf
https://www.uvm.edu/giv/resources/WGS84_NAD83.pdf

Why is this so complicated!?

The Earth's surface/shape is constantly changing
Our ability to measure the Earth's surface/shape and locations on the surface continues to improve (Thanks GNSS!)
The systems used to define coordinate systems and datums continues to evolve
The support for these systems in open-source tools continue to evolve, with a lot of confusing and/or outdated documentation out there on the web
There is a long (fascinating) history of surveying approaches, measurements, correction approaches, and definitions
Many legacy datasets use older CRS definitions
Many datasets have missing CRS information in metadata, sometimes incorrect information
The acronyms used for different CRS and datums can feel like alphabet soup: NAD83, WGS84, GRS80, NAVD88, EGM, ITRF

What is a CRS?

How are they defined?

https://uwgda-jupyterbook.readthedocs.io/en/latest/modules/04_Vector1_Geopandas_CRS_Proj/04_Vector1_Geopandas_CRS_Proj_demo.html#crs-and-projections

EPSG codes vs. proj strings vs WKT

Horizontal CRS

Ellipsoid models

https://proj.org/en/9.2/_images/general_ellipsoid.png

Vertical CRS

Geoid models

Projections

ITRF Realizations

epochs, time and plate deformation models

Plate motion ~1-8 cm/yr

Specific notes for North America

Transformations

Allows you to go back and forth between different CRS
You've all done this - convert from cartesian to polar coordiantes (high school math)
Can be 2D or 3D
Most open-source packages depend on PROJ library (https://proj.org/) for CRS support and transformations

Vector

pyproj: Python interface for PROJ
GeoPandas uses pyproj under the hood for CRS transformations, with support for compound 3D CRS

Raster

gdalwarp with proper CRS definitions (and available vertical offset grids) should work

Common datasets and CRS definitions

ICESat-2

Raster DEMs

ArcticDEM/REMA/EarthDEM products from PGC

These are distributed as 2D projected CRS (EPSG:3031 or EPSG:3413), without a vertical datum definition
Elevation values are "height above the WGS84 ellipsoid" - but no details about specific realization used by vendor (Maxar) providing source stereo imagery
Most of the Maxar data were acquired and delivered after 2008, so should be using more modern realizations of ITRF (2008, 2014, 2020), which are similar
Can likely assume ITRF2014 for most of the available DEM products
Can use custom WKT2 definintions for these 3D CRS:
- Antarctica: https://github.com/ICESat2-SlideRule/sliderule/blob/cb8ead40d761c8d637397a28e7b6d53fcf1de3c4/plugins/pgc/plugin/ITRF2014_3031.wkt
- Arctic: https://github.com/ICESat2-SlideRule/sliderule/blob/cb8ead40d761c8d637397a28e7b6d53fcf1de3c4/plugins/pgc/plugin/ITRF2014_3413.wkt

Copernicus 30 m DEM

EPSG:9518 (WGS84 + EGM2008)

Point clouds and altimetry

3DEP lidar

NAD83(2011) horizontal with NAVD88 vertical datum
Projection is Local UTM Zone
EPSG:6339+5703 (example for UTM Zone 10N, https://epsg.io/6339)
- Note: this is not the same as EPSG:32610 (WGS84) or EPSG:26910 (NAD83), because we are using NAD83(2011) realization

WA DNR

EPSG:2926+5703 (WA state plane N)
EPSG:2927+5703 (WA state plane S)
NAVD88 model should be geoid2012 (I think, need to confirm)

Examples

Setup

Updated to latest PROJ (>9.2 required for improved North American datum support)
Retrieve the vertical datum offset grids for your area of interest with https://proj.org/en/9.2/apps/projsync.html projsync --all

Check your dataset metadata

gdalinfo
Review documentation, lidar reports, etc.

ICESat-2 to other CRS

# Fake some 3D data but with epsg:4326
gf_orig = gpd.GeoDataFrame(geometry=gpd.points_from_xy([-120.4], [48.6], [1400]), crs='EPSG:4326')

# override 4326 with 3D CRS and do a 3D transform (uses pyproj under the hood):
gf_new = gf.set_crs(epsg=7912, allow_override=True)

gf_new.to_crs(epsg="2927+5703")

Other CRS to ICESat-2

Testing and validation

vdatum (https://vdatum.noaa.gov/)

`cs2cs`

echo -120.4 48.6 1400 | PROJ_DEBUG=2 PROJ_NETWORK=ON cs2cs -f "%.3f" -r epsg:7912 epsg:2927+5703

`projinfo`

projinfo -s EPSG:7912 -t EPSG:2927+5703 -o PROJ --hide-ballpark --spatial-test intersects

    Candidate operations found: 5
-------------------------------------
Operation No. 1:
unknown id, Inverse of Conversion from ITRF2014 (geocentric) to ITRF2014 (geog3D) + ITRF2014 to NAD83(2011) (1) + Inverse of Conversion from NAD83(2011) (geog3D) to NAD83(2011) (geocentric) + NAD83(2011) to NAVD88 height (3) + Inver
se of NAD83(HARN) to NAD83(2011) (NADCON5, CONUS) + SPCS83 Washington South zone (US Survey feet), 0.105 m, United States (USA) - CONUS onshore - Alabama; Arizona; Arkansas; California; Colorado; Connecticut; Delaware; Florida; Geor
gia; Idaho; Illinois; Indiana; Iowa; Kansas; Kentucky; Louisiana; Maine; Maryland; Massachusetts; Michigan; Minnesota; Mississippi; Missouri; Montana; Nebraska; Nevada; New Hampshire; New Jersey; New Mexico; New York; North Carolina
; North Dakota; Ohio; Oklahoma; Oregon; Pennsylvania; Rhode Island; South Carolina; South Dakota; Tennessee; Texas; Utah; Vermont; Virginia; Washington; West Virginia; Wisconsin; Wyoming.
PROJ string:
+proj=pipeline
  +step +proj=axisswap +order=2,1
  +step +proj=unitconvert +xy_in=deg +xy_out=rad
  +step +proj=cart +ellps=GRS80
  +step +proj=helmert +x=1.0053 +y=-1.90921 +z=-0.54157 +rx=0.02678138
        +ry=-0.00042027 +rz=0.01093206 +s=0.00036891 +dx=0.00079 +dy=-0.0006
        +dz=-0.00144 +drx=6.667e-05 +dry=-0.00075744 +drz=-5.133e-05
        +ds=-7.201e-05 +t_epoch=2010 +convention=coordinate_frame
  +step +inv +proj=cart +ellps=GRS80
  +step +inv +proj=vgridshift +grids=us_noaa_g2018u0.tif +multiplier=1
  +step +inv +proj=gridshift +no_z_transform
        +grids=us_noaa_nadcon5_nad83_2007_nad83_2011_conus.tif
  +step +inv +proj=gridshift +no_z_transform
        +grids=us_noaa_nadcon5_nad83_fbn_nad83_2007_conus.tif
  +step +inv +proj=gridshift +no_z_transform
        +grids=us_noaa_nadcon5_nad83_harn_nad83_fbn_conus.tif
  +step +proj=lcc +lat_0=45.3333333333333 +lon_0=-120.5 +lat_1=47.3333333333333
        +lat_2=45.8333333333333 +x_0=500000.0001016 +y_0=0 +ellps=GRS80
  +step +proj=unitconvert +xy_in=m +xy_out=us-ft

Note the 0.105 m uncertainty

Gotchas and other notes

There is no perfect transformation approach, and all transformations have some uncertainty
- https://vdatum.noaa.gov/docs/est_uncertainties.html
There are many possible ways to go from one CRS to another, the PROJ pipelines allow you to control this
Many CRS (esp compound or 3D CRS) don't have EPSG codes - you can define the CRS with machine-readable, well-known text (use WKT2)

Other resources

Comparison of values with different versions of the NAVD88 geoid (geoid2018 vs geoid2012): https://gist.github.com/scottyhq/bf13033a9655f302e8f9dc9235daf9fc

ShashankBice / 3D_CRS_Transformation_Resources