Hello,
I am a Civil Designer (a non surveyor), trying to understand transformations.?ÿ I am looking for confirmation that my below understanding of the procedure for transformation between datumA to datumB is a reasonable one, although conceptual.
Transformation of Vertical Datum (DatumA=>DatumB)
State Plane MapA (orthometric height)->GeoidA (orthometric height)->ellipsoidA (ellipsoid height)=> ellipsoidB (new ellipsoid height)-> GeoidB (orthometric height)-> State Plane MapB (orthometric height)
Transformation of Horizontal Datum (DatumA=>DatumB)
State Plane MapA (geodetic coordinate)->EllipsoidA (geodetic coordinate)=> EllipsoidB (geodetic coordinate)-> State Plane MapB (geodetic coordinate)
I'm not sure that I understand your question.
Orthometric Elevation = Ellipsoid Height- Geoid Height. In North America geoid heights are negative, so orthometric elevation is?ÿ always numerically greater than ellipsoid height.
Transforming locally between vertical datums is a simple addition/ subtraction operation.?ÿ?ÿ
This from the PIX4d website may help...
There is no direct mathematical relationship between horizontal datums.?ÿ There are only rubber sheet transformation models. There are different projection systems that points on a datum may be expressed in, and any coordinate system may be translated. But those are different things.?ÿ ?ÿ ?ÿ
For the US, perhaps this might help: https://geodesy.noaa.gov/INFO/datums-transformations.shtml
Links from this site are to transformation tools including explanations.?ÿ
On the matter of height relationships to various reference surfaces, I use the generic relationship
h - H - N = 0 = zero ( ideally ) which can be rearranged to solve any one with respect to two others.
where
h = normal distance from the chosen reference ellipsoid to the point.
H = curved distance from the chosen reference geoid to the point.
N = distance from the reference ellipsoid to the chosen reference geoid. For more details on geoid models see: https://geodesy.noaa.gov/GEOID/index.shtml
There are different ellipsoids, and geoids and must be kept compatible. To derive an NAVD88-compatible height one uses a NAD83 ellipsoid height in combination with the hybrid GEOID18 model. ?ÿ
To obtain a height compatible with the new height system one uses an IGS 08 ellispsoid height and a gravimetric geoid like USGG 2012.?ÿ
As datums are changing in the US you might want to review the documents here: https://geodesy.noaa.gov/datums/newdatums/index.shtml
Technical reports written by Dr Dru Smith about the issues and including lots of nice equations are also available.
If you're using ArcGIS software (or possibly QGIS), here's what would be happening internally. The US has a different workflow than the general one, because different types of transformations are available. I'm going to use specific coordinate systems.?ÿ
Input: NAD83 (NSRS2007) / State Plane California V (US feet) + NGVD29 heights
Output: NAD83 (2011) / State Plane California V (US feet) + NAVD88
Step 1: Input is unprojected to latitude-longitude NAD83 (NSRS2007) + NGVD29 heights
Step 2: Convert NGVD29 heights to NAVD88 heights using VERTCON (latitude-longitude unchanged)
Step 3: 2D transformation using NADCON5 from NAD83 (NSRS2007) to NAD83 (2011) (vertical unchanged)
Step 4: Project NAD83 (2011) to State Plane California V (vertical unchanged)
The NADCON5 and VERTCON (also GEOCON/GEOCON11) methods use files of offsets which are interpolated.?ÿ
The workflow you listed using ellipsoid heights would occur if you were changing geoid models or offset files were not available for a particular transformation. For example, if you were converting ITRF2014 to NAD83 (2011), you would use what I call an 'equation-based' method which needs ellipsoid heights, not gravity-related ones.
Maybe take a look at this presentation which is just the slides, not a recording but may give you a little insight.
Melita
Disclosure: I work for Esri.
