Identifying Ellipsoid Height from known coordinates

allenaggie · February 9, 2023, 8:56pm

Hello Emlid community,

I’d appreciate input on the process for identifying the Ellipsoidal Height for a known set of coordinates. I could be overcomplicating this, and am probably overlooking something, but I’ve spent a bunch of time and don’t quite nail it with the tools I am using, so I thought I’d seek input from this experienced group.

Here is a known monument as an example, in Rockwall Texas, from their GIS site.

Northing 7032885.954

Easting 2590432.919

Latitude N 32° 56’ 43.44684"
Longitude W 96° 28’ 20.68730"

Elevation 527.08

Date_Recorded September 6, 2017
Projection NAD 1983 (2011) TEXAS NORTH CENTRAL ZONE (4202)
Elevation_Datum_Projection NAVD88-GEOID12B

Convergence_Angle 01° 06’ 21.00438"
Grid_Scale_Factor 0.99987433
Combined_Scale_Factor 0.99985311

Besides setting my RS2+ up to take observations over the point, what’s the best tools/process to use, to take coordinates like these and produce an accurate ellipsoid height?

Much appreciated!

Jeff

kseniia.suzdaltseva · February 10, 2023, 8:35pm

Hi Jeff,

You can do it right in the Emlid Flow app:

Create a project in NAD83(2011) / Texas North Central and NAVD88(GEOID12B) height
Add a new point by entering its Local coordinates

Emlid Flow will calculate the point’s Geographic coordinates, including the ellipsoidal height, automatically

PatrickMcG · February 11, 2023, 9:15pm

Jeff,

Have you tried using the NGS NCAT tool? Here’s a link to the site:

https://geodesy.noaa.gov/NCAT/

Patrick

EBE111057 · February 12, 2023, 4:37pm

From NCAT “about” web page

“Please note that, although either orthometric or ellipsoidal heights can be used as inputs to NCAT, at this time NCAT does not convert between orthometric and ellipsoidal heights. Only orthometric-to-orthometric and ellipsoidal-to-ellipsoidal height transformations are currently possible in NCAT”.

You can also use the NGS geoid height processor for various flavors of “N”.

h= H + N

where “h” is the ellipsoid height

“H”= orthometric height

“N”= geoid height (various models)

The formula above is the simplified version and does not take into consideration deflection of the vertical and gravimetric effects.

https://geodesy.noaa.gov/GEOID/

In your case above, you want to determine the ellipsoid height. From the formula above, we can determine the height.

From the NGS computation, it gives a value of -25.478m, 0.046m error at 95% confidence level. The error is based on the density of passive stations with orthometric heights determined by differential leveling.

Output from GEOID12B is in meters -25.478m. We need “ftUS” though. 1m = 3.280833333 ftUS

-25.478 *3.280833333 = -83.589 ftUS

h= 527.08 ftUS+ (-83.589 ftUS)

h= 443.491 ftUS (ellipsoid height)

allenaggie · February 13, 2023, 2:03pm

Hey Patrick, I did but couldn’t quite get what I was looking for the reason Bryan mentioned.

allenaggie · February 13, 2023, 2:25pm

Bryan, great explanation. I missed the Geoid computation page - I spent a bit of time on the NGS Geoid models page, but the link to access the computation page was under tools: https://geodesy.noaa.gov/GEOID/GEOID18/computation.html

“N” is what I was seeking! Thank you for your response.

allenaggie · February 13, 2023, 2:29pm

Thanks Kseniia - the answer from Emlid was under my nose the entire time!

This community is great - I’ve got tools to quickly arrive at a solution and knowledgeable folks to help gut check how we got there.

EBE111057 · February 13, 2023, 3:34pm

Keep in mind that there are different flavors of “N”. From you first post the orthometric height is based on Geoid12B.

You can’t mix different geoids to determine ellipsoid heights.

https://geodesy.noaa.gov/GEOID/GEOID12B/

The link you show is for Geoid18

allenaggie · February 13, 2023, 4:56pm

Yep, that was an oversight, thank you for catching that. For Geoid 12B

I assume that is the one you used.

Geoid 18 is giving the same N but I understand not to mix them.